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We developed a new theory-based azimuthal phase retardation microscope to visualize distributions of actin filaments in biological cells without having them with exogenous dyes, fluorescence labels, or stains. The azimuthal phase retardation microscope visualizes distributions of actin filaments by measuring the intensity variations of each pixel of a charge coupled device camera while rotating a single linear polarizer. Azimuthal phase retardation δ between two fixed principal axes was obtained by calculating the rotation angles of the polarizer at the intensity minima from the acquired intensity data. We have acquired azimuthal phase retardation distributions of human breast cancer cell, MDA MB 231 by our microscope and compared the azimuthal phase retardation distributions with the fluorescence image of actin filaments by the commercial fluorescence microscope. Also, we have observed movement of human umbilical cord blood derived mesenchymal stem cells by measuring azimuthal phase retardation distributions.