Poly(3,4-ethylenedioxythiophene) coated Manganese Dioxide (PEDOT/$MnO_2$) composite electrode was fabricated by simply immersing the $MnO_2$ electrode in an acidic aqueous solution containing 3,4-ethylenedioxythiophene (EDOT) monomers. Analysis of open-circuit potential of the $MnO_2$ electrode in the solution indicates the reduction of outer surface of $MnO_2$ to dissolved $Mn^{2+}$ ions and simultaneously oxidation of EDOT monomer to PEDOT on the $MnO_2$ surface to form a PEDOT shell via a galvanic displacement reaction. Analysis of cyclic voltammograms and specific capacitance of the PEDOT/$MnO_2$, conductive carbon added $MnO_2$ and conductive carbon added PEDOT/$MnO_2$ electrodes suggests that the conductive carbon acted mainly to provide a continuous conducting path in the electrode to improve the rate capability and the PEDOT layer on $MnO_2$ acts to increase the active reaction site of $MnO_2$.