For the nonlinear distortion problem of current power amplifiers (PAs) with memory effects, we use goal programming to present a memoryless predistorter matrix model based on limiting baseband predistortion technique, and the normalized mean squared error (NMSE) is limited in a satisfactory range while the output power is maximum. Then we propose a nonlinear power amplifier with memory effects based on back propagation neural network (BPNN) with three tapped delay nodes and six single hidden layer nodes, which is single input - dual output. Simulation results show that the method proposed in this paper makes the experimental precision higher. Further, the linearization effect of power amplifiers becomes better.