The nanocomposites of polypyrrole (PPy) and multi-walled carbon nanotube (MWCNT) with different composition are synthesized by the chemical oxidative polymerization method. In these composites, the MWCNTs are uniformly coated by PPy with different thickness. The electrochemical properties of the composite electrodes are investigated by cyclic voltammetry, galvanostatic charge-discharge cycling and electrochemical impedance spectroscopy. The full cells assembled with the PPy/MWCNT composite electrodes deliver initial specific capacitances ranging from 146.3 to 167.2 F/g at 0.5 mA/$cm^2$ and exhibit stable cycling characteristics. The effect of content of MWCNT in the composite on cycling performance of the cells is also investigated.