You may need to do a hard reset of your iPhone. After reaching a full charge, unplug it and and check the usage log in a couple hours (make sure the screen is locked when not in use during that time), found in Settings > General > Usage at the bottom. If the Usage and Standby times are identical, you need to do a hard reset. Something is running continuously in the background that isn't supposed to be.
To do a hard reset, first press the home button and keep it held down. While holding that down, press the lock button up top and keep both of those pressed down until the Apple logo appears. Do not release before then! This takes perhaps 10 seconds. Your phone will then do a reboot that takes another 10-20 seconds perhaps. This should clear up the problem.