We investigated the magnetic and ferroelectric properties of orthochromite SmCrO3 by using density functional theory simulations. The atom coordinates of both Pbnm and Pna2(1) were calculated, and Pna2(1) was found to be the ground state structure. The spontaneous polarization in Pna2(1) structure is sensitive to delicate structure change which is induced by different antiferromagnetic order, and its direction is along the c axis. The spin structure of Pbnm was analyzed and it was found to not support ferroelectricity. The results revealed the origin of ferroelectricity of multiferroic SmCrO3 and explained the magnetoelectric effect.