A measurement error equation and a relative error analysis method for the Mueller matrix measurement technique based on a single photo-elastic modulator are proposed. Considering the relative error and the condition number, two optimum angle sets for the quarter-wave plate are obtained, which diminish the maximum relative error of each element of the Mueller matrix. The experimental results show that the maximum relative errors of each element of the Mueller matrix of the measured quarter-wave plate are 0.12% and 0.20% respectively by using the two optimum angle sets above. Compared to the maximum relative error of 0.83% of the traditional optimum angle sets {-90°,-45°,30°,60°} for the quarter-wave plate, the maximum relative errors of each element of the Mueller matrix of the measured quarter-wave plate are decreased by 85.54% and 75.90% respectively by using the two optimum angle sets above.