In order to eliminate the narrowband interference,a new recurrent neural network predictor(RNNP) based on the adaptive Kalman filter(AKF) was proposed in the spread spectrum system in this paper. The adaptive Kalman filter was used to modify the weights of the RNNP and precisely estimate the interference,with the virtue of rapid convergence rate,high prediction precision and perfect numerical robustness. Simulation results show that the RNNP based on AKF learning algorithm has improvement to different extent on interference elimination capability compared with the adaptive linear least mean square(LMS) interference predictor,the adaptive approximate conditional mean(ACM) interference predictor and the RNNP based on the real-time recurrent learning(RTRL) arithmetic.