The electrochemical performances of an asymmetric hybrid capacitor were investigated using $LiFePO_4$ as the positive electrode and active carbon fibers(ACF) as the negative electrode. The electrochemical behaviors of a nonaqueous hybrid capacitor were characterized by constant current charge/discharge test. The specific capacitance using $LiFePO_4$/ACF electrode turned out to be $0.87F/cm^2$ and the unit cell showed excellent cycling performance. This hybrid capacitor was able to deliver a specific energy as high as 178 Wh/kg at a specific power of 1,068 W/kg.