GPS receivers are susceptible to jamming by interference. This paper proposes a recurrent neural network (RNN) predictor for new application in GPS anti-jamming systems. Five types of narrowband jammers, i. e. AR process, continuous wave interference (CWI), multi-tone CWI, swept CWI, and pulsed CWI, are considered in order to emulate realistic conditions. As the observation noise of received signals is highly non-Gaussian, an RNN estimator with a nonlinear structure is employed to accurately predict the narrowband signals based on a real-time learning method. The node decoupled extended Kalman filter (NDEKF) algorithm is adopted to achieve better performance in terms of convergence rate and quality of solution while requiring less computation time and memory. We analyze the computational complexity and memory requirements of the NDEKF approach and compare them to the global extended Kalman filter (GEKF) training paradigm. Simulation results show that our proposed scheme achieves a superior performance to conventional linear/nonlinear predictors in terms of SNR improvement and mean squared prediction error (MSPE) while providing inherent protection against a broad class of interference environments.