Density functional calculations have been tremendously useful in understanding the microscopic origin of multiferroicity and in quantifying relevant properties in many multiferroics and magnetoelectrics. Here, we focus on a relatively new and promising compound, PbNiO 3 . The structural, electronic and magnetic properties of its two polymorphs, i.e. the orthorhombic structure with space group Pnma and the rhombohedral LiNbO 3 -type structure with space group R3c have been studied by using density functional calculations within DFT+U and hybrid functional schemes. Our data convey an accurate description of the pressure-induced phase transition from the rhombohedral to orthorhombic phase at a predicted critical pressure of 5 GPa in agreement with the measured value of 3 GPa. Both phases show the G-type antiferromagnetic configuration as a magnetic ground state, but differ in the spatial anisotropy associated with nearest-neighbor exchange couplings, which is strongly weakened in the rhombohedral LiNbO 3 -type phase. The predicted large ferroelectric polarization of the rhombohedral phase (Hao et al 2012 Phys. Rev. B 014116) has been reexplored and analyzed in detail using partial density of states, Born effective New J. Phys. 16 (2014) 015030 X F Hao et al charge tensors, charge density difference, electron localization function analysis and distortion mode analysis. The asymmetric bonding between the Pb 6s and O 2p orbitals along the [111]-direction is responsible for the polar cationic displacement, giving rise to a predicted large ferroelectric polarization as high as ∼100 µC cm −2 .