It could be the alternator, but it could also be that the battery has a shorted or partially-shorted cell, demanding too much curent from the alternator. Take it to anyplace that sells batteries, and they should be able to twll which it is in no time.

1977 CJ-7, fiberglass body, AMC 360 w/ headers, DUI ignition, Edelbrock intake and Holley 4150 carb, TF999, Dana 300, 4.56 gears lockers, York air comp, 4" susp lift, 2" body lift, BFG 35" M-T tires, Megashifter, AGR pump & box, REP8000 winch.