High-quality, large-area graphene films with few layers are synthesized on commercial nickel foams under optimal chemical vapor deposition conditions. The number of graphene layers is adjusted by varying the rate of the cooling process. It is found that the capacitive properties of graphene films are related to the number of graphene layers. Owing to the close attachment of graphene films on the nickel substrate and the low charge-transfer resistance, the specific capacitance of thinner graphene films is almost twice that of the thicker ones and remains stable up to 1000 cycles. These results illustrate the potential for developing high-performance graphene-based electrical energy storage devices.