Abstract: High power amplifier often brings a nonlinear distortion for the orthogonal frequency division multiplexing system in the transmitter. Diagonal Recurrent Neural Network (DRNN) is a modified model of the fully connected recurrent neural network with the advantage in capturing the dynamic behavior of a system. In this paper. DRNN is introduced to compensate transmitted signal before the signal passes the high power amplifier. The algorithm of gradient descent method is developed to train the DRNN, which requires a low amount of Random Access Memory (RAM) and is with much faster convergence speed from a blind start. The simulation shows that the network owns a rapid convergence and a low amount of RAM is required if this recurrent neural network is applied as predistorter.