This unfortunate side effect is known as "moon face" and typically occurs when you've been on the prednisone for an extended time or at high dosage. I don't know what condition you are using it for, but I would recommend seeking alternative therapies if at all possible. I had a reaction to an asthma drug in 2006 that almost killed me. I required massive doses of steroids for several days to save my life. The end result was holes in my memory, diabetes (that went away), radical mood swings (Jeckyll and Hyde kind of stuff) and a lot of other issues.
Prednisone is a sometimes necessary, but very nasty business. If you can get off of it, or get the dosage down that's ideal. If not, you'll probably end up with many side effects that don't go away completely until that garbage is out of your system. The "moon face" can also happen when developing Cushings Syndrome and that happens a lot in people who have been on prednisone for extended periods of time. I would ask your doctor to check to see what might be going on.