First-principals calculations show that magnetization reversal is accompanied by the opposite sense of rotation of the neighboring oxygen octahedra along the [1 1 1]direction which is called the antiferrodistortive displacement in BiCrO3.The coupling between magnetization and antiferrodistortive distortion is mainly caused by DzyaloshinskiiMoriya interaction which is driven by the eg-eg states antiferromagnetic interaction in Cr-3d.A critical value of on-site Coulomb interaction prohibiting the Dzyaloshinskii-Moriya interaction and thus the magnetization reversal is found to be 1.3 eV.