Using the first-principles pseudopotential method within a local density approximation of the density functional theory (DFT), the structural, electronic properties of SrS in the NaCl(B1) and CsCl(B2) structures have been studied. The calculated lattice parameters, bulk modulus and elastic constants are in excellent agreement with the experiment value and other theoretical value, whereas the minimum gap error is as high as 50.46% in the B1 structure. To get the reliable band gap values of the B1 structure, we employ the GW (G is Green's function and W is the screened Coulomb interaction) approximation method. The result in GW approximation improves the band gap value of the B1 structure greatly and agrees with the value of experimental measurement. And we also predict the band gap value of the B2 structure reliably by GW approximation.