Based on the measurement principle and the method of Mueller matrix and Stokes vector, the phase retardation and fast axis azimuth of wave plate are measured rapidly and simultaneously. After the laser passing through the polarizer and the standard 1/4 wave plate, the standard right rotation circular polarized light is produced and then passes through the wave plate sample. The Stokes vector of the laser after passing through the sample is recorded by the Stokes polarimeter, and the phase retardation and fast axis azimuth are obtained simultaneously. The influences of standard 1/4 wave plate parameter error and system stability on measurement results are analyzed. By using this experimental system, the average standard deviations of the phase retardation and fast axis azimuth of wave plate are ±0.05° and ±0.03°, respectively. The experimental relationship between the parameters of mica wave plate and quartz wave plate and temperature is also obtained. The proposed method has the characteristics of simple measurement process, high precision and real-time measurement of phase retardation and equivalent fast axis azimuth of unknown anisotropic material.