First, use a good cloth to clean your proximity sensor real good and see if that fix it.
This is a very typical problem when proximity sensor got dusty. Options are limited:
1. Blow compressed air into ear phone plug, it may blow away the dust.
2. Disassemble the phone to clean the sensor.
3. Root the phone and edit sensor configurations so it is set to wake up at higher values from proximity sensor.
4. Wait for miracle to happen and the phone heals itself.
My note 3 had this problem, I tried 1, didn't work, I didn't want to try 2 or 3 due to warranty.
6 months late, 4 worked!
@T-Mobile GN3