We propose a systematic approach that can empirically correct three major errors typically found in the density functional theory (DFT) calculation within a local density approximation (LDA) simultaneously for a set of common cation binary semiconductors, such as III-V compounds -(Ga or In)X with X=N, P, As, Sb, and II-VI compounds (Zn or Cd)X, with X= O, S, Se, Te. By correcting (1) the binary bandgaps at high symmetry points Γ, L, X, (2) the separation of p and d orbital derived valence bands, and (3) conduction band effective masses to experimental values and doing so simultaneously for common cation binaries, the resulting DFT-LDA based quasi first-principles method can be used to predict the electronic structure of complex materials involving multiple binaries with comparable accuracy but much less computational cost than a GW level theory. This approach provides an efficient way to evaluate the electronic structures and other material properties of complex systems much needed for material discovery and design.