The principle of single-wedge crystal waveplate depolarizer is introduced and its performance analyzed by simulation with the help of Stokes vectors.Two-wedge crystal waveplate depolarizer is proposed and a comparison is made between these two types of depolarizers.The simulation results show that wedge crystal waveplate depolarizers can depolarize an optical beam completely when the diameter of the beam and the angle of the waveplate satisfy a certain relationship and the beam diameter required by the two-wedge depolarizer is only half of that by the single-wedge depolarizer.An application example of connection of an optical fiber to a two-wedge depolarizer is given at the end of this paper.