A method for realizing 2D single-shot measurements of birefringence parameters (including both retardation and optic axis orientation) of anisotropic materials using a simple recording setup and an efficient processing algorithm is proposed. The recording setup can be built simply by inserting a circular polarizer and a polarization beam splitter, respectively, in the object path and reference path of a conventional off-axis holographic imaging system, with no need for other adjustments. An algorithm for quantitatively retrieving the birefringence parameters from one single-shot hologram is proposed and demonstrated, in which a new quantity describing the birefringence, called complex birefringence parameter, is introduced, and a set of formulas used to extract the birefringence parameters is derived. Some experimental results are given for demonstrating the feasibility of the method that reveal that the method may provide another effective approach for investigating the birefringence properties of dynamic anisotropic materials, especially the birefringence induced by ultrafast pulse lasers.