• An INS/GPS integrated navigation solution is designed for GPS denial environments. • An adaptive-gain complementary filter is proposed for attitude estimation. • A function is introduced to suppress maneuvering acceleration under dynamics. • A position prediction method based on the improved ANFIS is proposed. • The GPS position increment rather than position error is chosen to be predicted. Aiming to improve the accuracy of navigation systems during GPS outages, this paper presents an adaptive-gain complementary filter for attitude estimation. With the introduction of the acceleration vector as the observation, system dynamic information is considered to handle the high-frequency interference caused by external acceleration. Meanwhile, this paper presents a position prediction algorithm based on fuzzy neural networks with velocity and GPS position increment as the desired outputs. A hybrid method of the Least Mean Square (LMS) and conjugate gradient method is utilized to tune the parameters. With a 160 s non-overlapping sliding window, a flight test has been done using the proposed methods during 240 s GPS outages. The results indicate that the attitude estimation algorithm (RMSE of 0.89° and 0.45° for roll and pitch angles) performed better than the Mahony algorithm, and position prediction errors are 0.93 m and 1.12 m for latitude and longitude respectively.