Silica-manganese oxides with a core-shell structure were synthesized via precipitation of manganese oxides on the $SiO_2$ core while varying the concentration of a precipitation agent. Elemental analysis, crystalline property investigation, and morphology observations using low- and high-resolution electron microscopes were applied to the synthesized silica-manganese oxides with the core-shell structure. As the concentration of the precipitating agent increased, the manganese oxide shells around the $SiO_2$ core sequentially appeared as $Mn_3O_4$ particles, $Mn_2O_3+Mn_3O_4$ thin layers, and ${alpha}-MnO_2$ urchin-like phases. The prepared samples were assembled as electrodes in a supercapacitor with 0.1 M $Na_2SO_4$ electrolyte, and their electrochemical properties were examined using cyclic voltammetry and charge-discharge cycling. The maximum specific capacitance obtained was 197 F $g^{-1}$ for the $SiO_2-MnO_2$ electrode due to the higher electronic conductivity of the $MnO_2$ shell compared to those of the $Mn_2O_3$ and $Mn_3O_4$ phases.