Can two blue eyed parents have a green eyed kid?

I have used the eye-color calculator and the only colors that can be produced from two blue-eyed parents should produce a blue-eyed child.  However eye color is a complex.  I have used your grandparents and your parents eye colors in the chart and it did not produce green.  Maybe someone else has a better explanation.

 P.S.  I selected your mom's eye color from "You"

and your dad's eye color as "Your Mate" 

The eye-color calculator is at the following link:

http://museum.thetech.org/ugenetics/eyeCalc/eyecalculator.html

Don't panic they are still both your parents. Eye colors are a very tricky trait and science has not found a 100% way of determining what ones eye color is going to be. They come close and are right on a very high percentage of the time, but there is always the exception.

First let's find out what they say about green eyes-

Green eyes are the product of moderate amounts of melanin. They are most often found among people of North and Eastern European descent, and to a lesser extent, in Southern Europe, parts of Central and South Asia.[1][2][3][4]. Green eyes are an uncommon eye color. In Iceland 88% of the population have green or blue eyes. Other ethnically Nordic countries like Sweden, Denmark, Germany, Norway, and (less) the Netherlands [5] have a high percentage of green eyes. The Pashtuns are often called "Hurry Ankehian Wallay": the green-eyed people.

Now here is a good explanation of the traits involved in determining eye color.

At birth, babies are usually born with blue colored eyes, regardless of the eye colors of their parents. At this early stage in life, newborns have not started to make a dark brown pigment called melanin in the irises of their eyes. As babies get older, their eye color may change when they start producing melanin in their irises. Melanin is also produced by the skin when it?s exposed to UV rays to protect against their harmful effects. This pigment also causes a suntan to develop by darkening skin color.

Similar to skin tone, the darker the eye color, the more melanin is present. Iris color falls along a spectrum from blue, which equates to a little melanin, to dark brown or even black, which equates to a lot of melanin. Gray, green, hazel, and lighter brown colored eyes fall in between these two ranges.

Eye color is a physical trait that is determined by the pairing of genes from both parents. It used to be thought that a single gene pair following dominant and recessive inheritance patterns was responsible for this trait. Now it is known to be much more complex, involving at least three gene pairs. Geneticists have focused on two of the three gene pairs to help clarify the inheritance of eye color: EYCL1 (the gey gene) and EYCL3 (the bey2 gene).

Genes come in different forms, called alleles. The gey gene has two alleles, green and blue; the bey2 gene has two alleles, brown and blue. The brown allele is always dominant over the green and blue alleles, the green allele is always dominant over the blue allele, and the blue allele is always recessive.

It is possible for two brown-eyed parents to have a child with a different eye color than theirs. For two brown-eyed parents to have a blue-eyed child, for example, the mother and father would need to pass on a pair of blue alleles each to their offspring. If this child were to get one green allele in this mix instead, s/he would have green eyes; however, if a brown allele is present, regardless of what the other three alleles are, the child would have brown eyes.

But wait, you say: this two gene model cannot explain the inheritance of gray or hazel colored eyes, nor can it explain how two blue-eyed parents can have brown-eyed progeny. It appears that as of yet to be determined modifier genes, other eye color genes, mutations, and/or possibly additional factors are involved in eye color inheritance.

So relax and enjoy your green eyes, they set you apart from many others.

Good luck and best wishes. 

Then your cat joins in having heterochromia along with some famous people. Heterochromia (also known as a heterochromia iridis or heterochromia iridium) is an ocular condition in which one iris is a different color from the other iris (complete heterochromia), or where the part of one iris is a different color from the remainder (partial heterochromia or sectoral heterochromia). It is a result of the relative excess or lack of pigment within an iris or part of an iris, which may be inherited or acquired by disease or injury.[50] This uncommon condition usually results due to uneven melanin content. A number of causes are responsible, including genetics such as chimerism and Waardenburg syndrome. Trauma and certain medications, such as some prostaglandin analogues can also cause increased or decreased pigmentation in one eye. On occasion, the condition of having two different colored eyes is caused by blood staining the iris after sustaining injury.

David Bowie (Jones) is a famous person often wrongly attributed with heterochromia. His apparent condition is due to a teenage injury. (One eye appears darker because the pupil is permanently dilated.) American actress Kate Bosworth has sectoral heterochromia, resulting in a hazel section at the bottom of her right blue eye, while the left is completely blue. American Actress Elizabeth Berkley has sectoral heterochromia; her right eye is half green and half brown, and her entire left eye is green. The lead vocalist of American band Rise Against, Tim McIlrath, has heterochromia; his left eye is blue while his right is brown. American actress Mila Kunis also has heterochromia, resulting in one green eye and one brown eye. American Actress Demi Moore also has heterochromia, by having one green eye, and the other hazel.

Best wishes. 

My ex-husband and I both have blue eyes, but both of our two children have green eyes.

He has NO green-eyed people in his family, and I only have two people in my entire family that have green eyes, everyone else's eyes are blue, except for my dad's whose eyes are brown.

Yes