A measurement technique for the Mueller matrix based on a single photo-elastic modulator is proposed to improve the current measurement methods. An optimization algorithm and a two-step procedure of system parameter calibration are also presented. System parameters are calibrated by the two-step calibration procedure. Then, the Mueller matrix of the measured sample is obtained with the optimization algorithm. The experimental results show that the retardation and the fast axis angle of the measured quarter-wave plate are 90.4185° and 0.2348°, respectively. The corresponding errors are less than the retardation tolerance λ/300 and the maximum rotation error 0.4°, respectively. Compared to the standard Mueller matrix of a quarter-wave plate whose fast axis angle is set at 0°, the maximum relative errors of each element of the Mueller matrix of the measured quarter-wave plate are 1.97% and 0.83% with direct and indirect measurement method, respectively. Both errors are less than 2.11%, which is the simulation value of the maximum relative error. Decreasing the retardation tolerance or improving the precision of the rotation stage can diminish the maximum relative error of each element of the Mueller matrix.