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. For other users, logging out of iCloud and logging in again after a restart solved the battery drain.
Try to force restart 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
Did you already visit an Apple Authorized Service Provider and let them check the battery? Depending on the age and use of the phone, it might be time to get it replaced. As Apple does not sell spare parts for the iPhone, you should Apple let replace the battery. Your carrier might also be authorized by Apple to do that.
Service Answer Center - iPhone
Find an Apple Authorized Service Provider
Contact your carrier
Maybe also take a look at this page about battery drainage