In biological and medical sciences, optical microscopes are widely used. By using the microscope, we can observe cellular dynamics including intracellular ions and molecules tagged with fluorescent dyes at a high magnification. However, a freely motile cell easily escapes from a field of view and a focal plane of the typical microscope. Therefore, we propose a novel auto-focusing (AF) algorithm and develop an AF and tracking microscope. XYZ positions of a microscopic stage are visual feedback controlled to focus and track the cell automatically. A bright-field image is used to estimate a cellular position. XY centroids are used to estimate XY positions of the tracked cell. To estimate a Z position, we use a diffraction pattern around the cell membrane. This estimation method is so-called Depth from Diffraction (DFDi). However, this method is not robust for individual differences between cells because the diffraction pattern depends on each cellular shape, reflective index and transparency. Therefore, in this study, we propose a real-time correction of DFDi by using 2D Laplacian of a center region of the cell as a goodness of the focus. To evaluate the performance of our developed algorithm and microscope, we auto-focus and track a freely moving paramecium. In this experimental result, the paramecium is auto-focused and kept inside the scope of the microscope during 45s. The evaluated focal error is within 5[µm], while a length and a thickness of the paramecium are about 200[µm] and 50[µm], respectively.