Quantitative three-dimensional imaging of cells can provide important information about their morphology as well as their dynamics, which will be useful in studying their behavior under various conditions. There are several microscopic techniques to image unstained, semi-transparent specimens, by converting the phase information into intensity information. But most of the quantitative phase contrast imaging techniques is realized either by using interference of the object wavefront with a known reference beam or using phase shifting interferometry. A two-beam interferometric method is challenging to implement especially with low coherent sources and it also requires a fine adjustment of beams to achieve high contrast fringes. In this letter, the development of a single beam phase retrieval microscopy technique for quantitative phase contrast imaging of cells using multiple intensity samplings of a volume speckle field in the axial direction is described. Single beam illumination with multiple intensity samplings provides fast convergence and a unique solution of the object wavefront. Three-dimensional thickness profiles of different cells such as red blood cells and onion skin cells were reconstructed using this technique with an axial resolution of the order of several nanometers.