To solve the problem that fracturing effect is not perfect in the practical applications of coal constant pressure water injection, based on the application of FLAC3D computer simulation to the rock and soil mechanics, the crack initiation process of the coal on the conditions of pulsatile and constant pressure water injections is simulated, the induce-crack characteristics of the coal on the conditions of pulsatile and constant pressure water injections are analyzed. The results of numerical simulation show that after hydraulic fracturing, the fracturing radius of the strike direction in the model of pulsatile water injection is 3.3m, the fracturing radius of the vertical direction is 2.2m; the fracturing radius of the strike direction in the model of constant pressure water injection is 0.65m, the fracturing radius of the vertical direction is 0.96m. The coal needed more time to crack initiation on the condition of pulsatile water injection than that of constant pressure water injection, the ultimate compressive stress for the model of the pulsatile water injection is lower than that for the model of the constant pressure water injection, a conclusion that the pulsatile water injection is significantly better than the constant pressure water injection in the pressure relief of the coal-rock is drawn.