Electronic band-structure calculations have been performed for zinc-blende A$III$B$V$ (AlP, AlAs, AlSb, GaP, GaAs, GaP, InP, InAs, InSb) and A$II$B$VI$ (ZnS, ZnSe, ZnTe, CdS, CdSe, CdTe) semiconductors by the ab initio pseudopotential method within the local-density approximation (LDA). The lattice parameters, band gaps, Luttinger parameters, momentum matrix elements and effective masses are studied in detail. It is shown that LDA calculations cannot give accurate band parameters systematically. It is found that LDA band parameters calculated using the experimentally determined lattice constants are more accurate than those using the LDA lattice constants. We found that inclusion of $d$-electrons of group-II atoms into the core gives more accurate band parameters.