A novel adaptive digital pre-distortion algorithm with Volterra kernel is provided. According to the error threshold, corresponding convergent process is selected to compensate coefficients of OFDM power amplifier. When the error signal is big, adaptive algorithm with high speed convergence will be picked up. Otherwise,the pre-distorter coefficients updating base on a smooth convergent process which is propitious to hardware implementation to trace the time variability of nonlinear power amplifier and compensate nonlinear effect with memory. Therefore, cost of digital adaptive pre-distortion system can be saved and hardware implementation could be facile.