In view of the failure of GNSS signals, this paper proposes an INS/GNSS integrated navigation method based on the recurrent neural network (RNN). This proposed method utilizes the calculation principle of INS and the memory function of the RNN to estimate the errors of the INS, thereby obtaining a continuous, reliable and high-precision navigation solution. The performance of the proposed method is firstly demonstrated using an INS/GNSS simulation environment. Subsequently, an experimental test on boat is also conducted to validate the performance of the method. The results show a promising application prospect for RNN in the field of positioning for INS/GNSS integrated navigation in the absence of GNSS signal, as it outperforms extreme learning machine (ELM) and EKF by approximately 30% and 60%, respectively.