By employing the linearized muffin-tin orbital (LMTO) GW approach, core-valence correlation efects on the quasi-particle electronic structures are investigated for GaAs and CdTe possessing semi-core d-electrons. The contributions from these d-electrons to the dielectric function and the energy band gap are examined, and the quasi-particle energies of semi-core levels aredetermined. The semi-core correlation effects are found to be non-negligible in determining the energy band gap: the magnitudes of correlation effects on the band gap amount to 0.1 and 0.2 eV for GaAs and CdTe, respectively, suggesting that the correlation effects of semi-core d-electrons should be taken into account properly in the GW calculation. Further, the quasi-particle energy positions of semi-core d-levels obtained by treating those electrons as valence band are in excellent agreement with experiments.