We report the understanding of the electronic band structure of $Cs_4CuSb_2Cl_{12}$ perovskite through first-principles density-functional theory calculations. We find that the most stable state has the antiferromagnetic configuration where each $[CuCl_6]$ octahedral chain along the [010] direction is antiferromagnetic. The reasonable band structure of the compound can be obtained only if both the correct magnetic order and the improved exchange interaction of the Cu $it{d}$ electrons are taken into account.