This is what I found:
Whether or not you can get a passport with a felony conviction depends on what you were convicted of and whether or not you are still under legal supervision. If you on probation or parole for your felony, you may not be allowed to travel without prior approval. If you have been convicted of a felony drug offense that involved crossing international borders, the State Department may deny you a passport if you are still under supervised release. You could then apply for an emergency or a humanitarian exception to get a passport issued, although there is no guarantee you can get one.
However, in most cases, you can still get a passport even with a felony conviction. Of course, once you have your passport, finding a country that will let you in may be a little bit harder. Some countries won't let you in if you have a criminal record, especially if you have a felony conviction. If you have a felony conviction, it would be a good idea to research the entry requirements for the country you're entering.
Also, make sure to allow enough time before your trip for your passport to be returned to you. Passport processing currently takes over 6 weeks for regular processing and 3 weeks for the government's expedited processing.
If you are nervous about applying for your passport, it might be worth going through a private passport expediting company, as well. They can help you with the paperwork, and can cut processing time down to anywhere from a little over a week to just 24 hours, depending on the option you choose when you order. The sooner you have your passport in hand, the sooner you can stop worrying about it and start planning your trip.