Abstract: For the linearization of orthogonal frequency division multiplexing (OFDM) power amplifiers, a digital pre-distorter is proposed to compensate for nonlinear distortion in this paper. The pre-distorter is realized by Volterra series, and a restarted BFGS algorithm is proposed for training of the nonlinear pre-distorter. Training of Volterra series can be switched between gradient descend algorithm and quasi Newton algorithm by setting a switching condition. This makes the new algorithm much more stable with a fast convergence rate. The pre-distorter is used for OFDM power amplifiers and it high efficiency is proved by simulation results. Moreover, the performance of OFDM power amplifiers is also improved by the pre-distorter.