The approximation expression of discrete data can describe the system well and clearly. Traditional approximation methods require a lot of data, so they are not suitable for poor data discrete nonlinear systems. In order to overcome the shortcomings of traditional methods, a generalized grey universal approximation method for poor data discrete nonlinear systems was proposed. First, subdivide the range of the discrete system as needed. Second, build the grey possibility function as the basis function. Third, use the curve fitting method to determine the weight of the basis function. The results of simulation supported the effectiveness of the model.