battery not charging but green light

Ok... well I know what your talkiing about, at least i think. Unplug it, does the bettery icon show that its 100% remaining, or is it literaly not charging. also check the side or bottom (if older MBP), there should be a small round button that blends with the computer,press it, it will show how many bars you got from 1-5 green dots should appear next to the small button. if it literaly isnt charging, try taking to a Genus Bar at an Apple store close by

Your machine may use the battery when it's plugged in, but only under extremely heavy load. At such times the machine requires more power than the AC adapter can supply, charging stops if it was going on, and the battery is drawn upon to make up the power deficit. This is usually seen when running extremely demanding games or doing other things that stress the GPU to its limits.

When the battery is full, the charging circuitry automatically stops charging, but the light remains green. This prevents overcharging and overheating of the battery. It will start charging again when the charge level falls below 95%.

Like eww said if it is fully charged, it will stop charging so not to waist energy or harm the battery.