In this study, a robust adaptive filter using fuzzy logic for tightly-coupled visual-inertial odometry (VIO) navigation system is proposed. First, the authors use the epipolar geometry and trifocal tensor geometry as the measurement models of the VIO navigation system, which can avoid calculating the three-dimensional position of feature points. Second, the camera poses corresponding to the three images are corrected in the filter to form a multi-state constraint Kalman filter. Finally, when the measurement noise statistics changes or the erroneous measurement occurs in practical applications, the proposed method utilises Takagi–Sugeno (T–S) fuzzy logic to determine a scalar factor according to the divergence degree parameter. Then, the scalar factor is applied to the innovation covariance matrix and the filter gain, which improves the navigation accuracy and robustness of the VIO navigation system. The experimental results testing with the publicly available real-world KITTI dataset demonstrate the effectiveness of the proposed method.