The nonlinearity of power amplifiers (PAs) limits the transmission efficiency of modern wireless communication systems. This problem becomes more challenging for the fifth generation (5G) cellular systems due to the extremely high peak-to-average ratio (PAPR) of signals. This paper proposes a nonlinear equalizer that combines a Volterra series model with a recurrent neural network called Nonlinear Autoregressive with eXogenous input model (NARX) neural network (NARXNN) to eliminate the nonlinear effects of PAs. In order to remove the nonlinear PAs distortion more effectively, the input features of NARXNN are designed according to the PA Volterra series model. Experiments are conducted with simulated data generated by SystemVue. The simulation results demonstrate that the proposed neural network based nonlinear equalizer has excellent performance even under the limited training set.