Abstract: The matrix Pade approximants based on generalized inverse is characterized by keeping approximation order and without multiplication of matrices in the construction process. In this paper, a new nonlinear approximating method for matrix exponential functions is established by means of this result. This method is obviously superior to the original Pade method because it can be applied to singular matrices and higher-order matrices, and the obtained algorithm is suitable to compute on computers. A computational example is given to illustrate the efficiency of the algorithm. Existence and uniqueness of approximation formulas are proven.