The electronic structures of the perovskite oxides, LaMnO₃ and CaMnO₃, with various magnetic structures are studied using the first-principles discrete variational (DV) cluster method based on ab initio local-spin-density approximation (LSDA). The ground states of different magnetic phases (including ferromagnetic (FM), A-type antiferromagnetic (A-AFM), and G-type antiferromagnetic (G-AFM)) have been described in this work. The cubic CaMnO₃ with observed G-AFM magnetic order is found to have a 0.1 eV calculated gap. Both FM CaMnO₃ and LaMnO₃ have "half-metallic" character, which is in agreement with other works. LaMnO₃ with both A-type and G-type antiferromagnetic order have metallic band structures. Part of Jahn-Teller (JT) distortion (Q₂ type) has been taken into consideration for A-AFM LaMnO₃. Under Q₂ type JT distortion, the occupied and unoccupied states of O 2p and Mn 3d states move farther away from the Fermi energy. It is also found that the distortion can further stabilize the structure. The density of states and the binding energy of the distorted A-AFM LaMnO₃ are given in this paper.