In this study, we have prepared, as the pluse power source, a commercially supplied Li-ion battery with a capacity of 700 mAh and AC resistivity of 60 md at 1 kHz and nonaqeous asymmetric hybrid capacitor composed of an activated carbon cathode and MCMB anode, and have examined the electrochemical characteristics of hybrid capacitor and the pulse performances of parallel connected hybrid capacitor/Li-ion battery source. The nonaqueous asymmetric hybrid capacitors constituted with each stack number of pairs composed of the cathode, the porous separator and the anode electrode were housed in Al-laminated film cell. The 10 stacked hybrid capacitor, which was charged and discharged at a constant current at 0.25 $mA/cm^2$ between 3 and 4.3 V, has exhibited the capacitance of 108F and the lowest equivalent series resistance was 32 $m{Omega}$ at 1 kHz. On the other hand, the enhanced run time of Li-ion battery assisted by the hybrid capacitor was obtained with increasing of current density and pulse width in Pulse mode. The best improvement, $84;\%$ for hybrid capacitor/Li-ion battery was obtained in the condition of a 7C-rate pulse (100 msec)/0.5C-rate standby/$10;\%$ duty cycle.