Aiming at the nonlinear characteristics and memory effects of power amplifier, a memory rational function behavioral model, which is based on the memory polynomial model and memoryless rational function model, is proposed. The model coefficients were identified by conjugate gradient method. The estimation of the best model nonlinearity order and the best memory depth was carried out with the minimized the normalized mean squared error (MNSE). The model was validated using multi-carrier WCDMA signal and a MRF6S21140H power amplifier by measurement. The result indicates that the proposed model can achieve better model performance with less number of coefficients, compared with the memory polynomial model and memoryless rational function model.