Based on the Stokes-Mueller matrix polarization algorithm, the polarization control mechanism of a biplate that consists of double quarter wave-plates or double 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. The movement trajectory of modulated polarization state on the Poincaré sphere was obtained. Which helps 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. The polarization control accuracy for the exiting Stokes vector was also analysed. For a biplate that the error along the fast axis direction is±2 ° and the retardance error is λ/300, the maximum measurement error of Mueller matrix is 0.040 2. 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.