The water entry problem of a wedge is simulated based on the velocity potential theory in time domain. The Complex Variable Boundary Element Method (CVBEM) is used in the stretched coordinate system. Before the simulation, the similarity solution is taken as the initial conditions. The auxiliary function scheme in conjunction with the same CVBEM is used to obtain the accurate time derivative of velocity potential and pressure distribution on wedge surface. The time marching solution is matched with the jet special treatment. Finally, the simulation results are compared with the similarity solution, which shows that the jet linear approximation can simulate the jet well.