The structural, electronic, and thermodynamic properties of the binary II-VI semiconductors CaS, ZnS and their alloy Ca_xZn_(1-x)S in the B_3 (zinc blend) phase are investigated to elaborate the effect of substitution of Ca in ZnS in the range 0 ≤ x ≤ 1. For this purpose, first principal density functional calculations are used via the full-potential linear muffin-tin orbital (FP-LMTO). The exchange and correlation energies are described in the generalized gradient approximation (GGA) and local density approximation (LDA). The effect of composition on the lattice constant, bulk modulus, and band gap is investigated. The equilibrium structural parameters for Ca_xZn_(1-x)S are obtained from the total energy minimization calculations. The electronic structures of Ca_xZn_(1-x)S are calculated and analyzed in terms of the contribution of the Zn s and p, S s, and Ca s and p states. Using the approach of Zunger and co-workers, the microscopic origin of the band gap bowing has been explained. The disorder parameter (gap bowing) is found to be mainly caused by the chemical charge transfer effect. The electron (hole) and valence effective masses are also calculated. Moreover, the thermodynamic stability of the studied alloys is investigated by means of the miscibility critical temperature.