Based on the Stokes-Mueller matrix polarization algorithm, the polarization control mechanism of biplate that consists of double single quarter wave-plates or half wave-plates was analyzed in detail. We have derived the analytical relations between the modulated polarization state and the fast-axis direction for the biplate and obtained the movement trajectory of modulated polarization state on the Poincaré sphere, which helped us to propose a polarization control measurement system using a biplate to complete the measurement of the Mueller matrix based on the projection matrix algorithm for the incident and exiting Stokes vectors and the analysis of polarization control accuracy for the exiting Stokes vector. Experimental results performed on such a biplate that the fast axis direction error is ± 2 °, and the retardance error is λ/300 demonstrated that the maximum measurement error of Mueller matrix is 0.0402, When the azimuth error caused by the error of the biplate is less than 0.16 rad, the elliptic angle error caused by the fast axis direction is not more than 0.032 rad, the ellipsometry error caused by the retardance is less than 0.015 rad, and it has no influence on the degree of polarization.