The structure and ground state electronic structure of the recently synthesized SrPdO3 perovskite [A. Galal et al., J. Power Sources, 195, 3806 (2010)] have been studied by means of screened hybrid functional and the GW approximation with the inclusion of electron-hole interaction within the testcharge/test-charge scheme. By conducting a structural search based on lattice dynamics and group theoretical method we identify the orthorhombic phase with Pnma space group as the most stable crystal structure. The phase transition from the ideal cubic perovskite structure to the Pnma one is explained in terms of the simultaneous stabilization of the antiferrodistortive phonon modes R + 4 and M + 3 . Our results indicate that SrPdO3 exhibits an insulating ground state, substantiated by a GW0 gap of about 1.1 eV. Spin polarized calculations suggests that SrPdO3 adopts a low spin state (t ↑↓↑↓↑↓ 2g e 0 g ), and is expected to exhibit spin excitations and spin state crossovers at finite temperature, analogous to the case of 3d isoelectronic LaCoO3. This would provide a new playground for the study of spin state transitions in 4d oxides and new opportunity to design multifunctional materials based on 4d Pnma building block.