Crystallized $LiMn_{2-y}Mg_{y}O_4$ powder was prepared by calcing the mixture of LiOH.$H_2O$, $MnO_2$ and MgO at $800^{circ}C$ for 36h in an air atmosphere. The structure of $LiMn_{2-y}Mg_{y}O_4$ crystallites was analyzed from powder X-ray diffraction data as a cubic spinel, space group Fd3m. Though all cathode material showed spinel phase based on cubic phase in X-ray diffraction, other peaks gradually exhibited and became intense with increasing y value in $LiMn_{2-y}Mg_{y}O_4$. However, ununiform which calculated by (111) face and (222) face was constant in spite of the increase of y value, except pure $LiMn_2O_4$. AC impedance of Li/$LiMn_{2-y}Mg_{y}O_4$ cells revealed the similar resistance of about $70Omega$ before cycling. In addition, The impedance of Li/$LiMn_{1.9}Mg_{0.1}O_4$ cell changed during charge and discharge or after cycling.