Probably apps running in the background are causing this, sometimes Mail get's stuck connecting to the mail server, or some social media app like Facebook can also be a reason for prolonged background activity.
Try to reset the phone by holding the sleep and home button for about 10sec, until the Apple logo comes back again. You will not lose any data by resetting, but it can cure some glitches.
If this does not help, setting it up as new device would be the next step:
How to erase your iOS device and then set it up as a new device or restore it from backups
Or, if you want to use your computer and iTunes instead:
Use iTunes to restore your iOS device to factory settings - Apple Support
Also take a look at these articles:
Apple - Batteries - Maximizing Performance
The Ultimate Guide to Solving iOS Battery Drain