CaS crystallizes in cubic NaCl (B1) type structure with symmetry Fm (3) over barm. In this work, the structural and electronic properties of CaS were investigated by considering the Density Functional calculations within the framework of Generalized Gradient Approximation (GGA) under high pressure. The structural change was found at the B1 type structure of CaS. B1 type structure transformed into another cubic CsCl (B2) type structure with symmetry Pm (3) over barm at 36.6 GPa. An intermediate state with symmetry R (3) over barm was predicted during this transition. Besides, the effects of the pressure on the electronic properties of CaS were also studied. Both the B1 and B2 type structures exhibited semiconducting behaviors with direct band gaps at the Gamma-point and R-point, respectively. Intermediate state was searched during this phase change first time in detail. The obtained results were compared with experimental and theoretical ones in the literature.