Polarization microscope is a useful technique to observe the optical anisotropic nature of biomedical specimens and provide more microstructural information than the conventional microscope. In this paper, we present a division of focal plane (DoFP) polarimeter based polarization microscope which is capable of imaging both the Stokes vector and the 3×4 Mueller matrix. The Mueller matrix measurement can help us completely understand the polarization properties of the sample and the Stokes vector measurement is a simultaneous technology. First, we calibrate a DoFP polarimeter using the polarization data reduction method for accurate Stokes vector measurements. Second, as the Stokes vector computation for all pixels using the calibrated instrument matrix is usually time consuming, we develop a GPU acceleration algorithm for real time Stokes vector calculations. Third, based on the accurate and fast Stokes vector calculation, we present an optimal 4-states of polarization (4-SoP) illumination scheme for Mueller matrix measurement using the DoFP polarimeter. Finally, we demonstrate the biomedical applications of the DoFP polarimeter based polarization microscope. Experiment results show that the characteristic features of many biomedical samples can be observed in the “polarization staining” images using the circularly polarized light as illumination. In this way, combined with GPU acceleration algorithm, the DoFP polarization microscope has the capacity for real time polarization monitoring of dynamic processes in biological samples.