To improve the seamless navigation ability of an integrated Global Positioning System (GPS)/inertial navigation system in GPS-denied environments, a hybrid navigation strategy called the self-learning square-root- cubature Kalman filter (SL-SRCKF) is proposed in this article. The SL-SRCKF process contains two innovative steps: 1) it provides the traditional SRCKF with a self-learning ability, which means that navigation system observations can be provided continuously, even during long-term GPS outages; and 2) the relationship between the current Kalman filter gains and the optimal estimation error is established, which means that the optimal estimation accuracy can be improved by error compensation. The superiority of the proposed SL-SRCKF strategy is verified via experimental results and prominent advantages of this approach include: 1) the SL-SRCKF comprises two cycle filtering systems that work in a tightly coupled mode, and this allows more accurate error correction results to be obtained during GPS outages; 2) the system's error prediction ability is effectively improved by introducing a long short-term memory, which provides much better performance than other neural networks, such as random forest regression or the recursive neural network; and 3) under different (30, 60, and 100 s) GPS outage conditions, the long-term stability of SL-SRCKF is much better than that of other error correction approaches.