Recent developments in epitaxial techniques have allowed for the growth of complex oxide heterostructures with unprecedented control over structural quality and chemical composition, with atomic layer precision.  For instance SrTiO3 with record high electron mobility has been achieved, and characteristics of 2 dimensional electron gas (2DEG) at the interface of two insulators such as LaAlO3 and SrTiO3 have been reported in the literature.  Despite the rapid progress basic parameters such as band gaps and band alignments of perovskite oxides, which are essential ingredients in the design of heterostructures based devices, are largely unknown.  Here first-principles calculations were used to investigate the electronic structure and band alignments of a series of perovskies ABO3, for varying both A and B cations.  The calculations were based on the density functional theory in both the generalized gradient approximations (GGA) and the hybrid functional formulation by Heyd-Scuseria-Ernzerhof (HSE) as implemented in the Vienna Ab-Initio Simulation Package (VASP).  While the GGA is know to severely underestimate band gaps, the HSE is expected to result in much more accurate values for both band gaps and band alignments.  The variation of band gaps and band alignments were rationalized in terms of the atomic orbital energies and atomic sizes.  This data will serve as the basis in the electronic structure design of complex oxide heterostructures with potential applications in novel electronic devices.