A Mueller-matrix polarimeter in transmission mode using two electronically controlled liquid-crystal variable retarders has been developed. Its design, theory and calibration are described. Although liquid crystals have been proposed earlier, this paper is focused on the process of the calculation of the Mueller matrix by a matrix-inversion method, oriented to static systems and in vitro samples. By driving the retarders with appropriate voltages, nine independent pairs of polarization states can be produced (incomplete polarimetry), while the other additional seven pairs are obtained by placing two quarter-wave plates (in the input and output optical paths respectively). This configuration allows extraction of 16 independent measurements of intensity. The Mueller matrix of the sample is calculated from them. The results of Mueller matrices for air, a linear polarizer and a quarter-wave plate are presented. Additional polarization parameters such as retardation, ellipticity or degree of polarization were also computed and some applications of the system are proposed.