The electronic band structures of zinc-blende ZnTe and CdTe are calculated by using a self-consistent full-potential linearized augmented plane-wave method within the first-principle formalism. In order to clarify the electronic properties near the Brillouin-zone (BZ) center and give an effective guideline on the material design for electronic and optical devices, we link the first-principle band calculations with the effective-mass approximation. The electronic properties are analytically studied on the basis of the effective-mass Hamiltonian for zinc-blende symmetry. The effective-mass parameters, such as crystal-field splitting, spin-orbit splitting, electronic effective mass,and the hole effective mass and the corresponding Luttinger-like parameters, are determined by reproducing the calculated band structures near the BZ center. The obtained results are in good agreement with available experimental and theoretical values.