The structural evolution, electronic and magnetic properties of the high-pressure nonpolar orthorhombic phase (orthorhombic, space group Pnma) and the LiNbO3-type (rhombohedral, space group R3c) InFeO3 have been explored via first-principles calculations. Furthermore, the ferroelectric properties of the LiNbO3-type phase have been revisited thoroughly. First of all, the nonpolar orthorhombic phase crystallized within Pnma space group was theoretically recognized. Secondly, the results reasonably reproduced the pressure-induced R3c →Pnma structural phase transition, which is in fair agreement with the experimental observation that the LiNbO3-type phase can be achieved from the decompression of the high pressure perovskite phase. In addition, the electric polarization for the non-centrosymmetric LiNbO3-type within the G-type antiferromagnetic ground state is evaluated to be 86.5 μC/cm2 by means of the Berry phase formula. More interestingly, in conjunction with the geometric factor, an additional mechanism behind the ferroelectric displacement is clarified as the strong chemical bonding between the In 5s and O 2p orbitals, i.e., the hidden tendency to create space for the unoccupied antibonding states, independent of whether the cation is an s0 or s2 configuration, and is manifested in terms of the analysis of Born effective charges, potential energy surfaces, charge density isosurfaces.