In order to improve the ability of mobile robots to navigate autonomously in unknown environments, a novel visual-inertial SLAM fusion method based on the kernel function threshold adaptive adjustment strategy and the Levenberg-Marquardt algorithm is proposed. First, in order to reduce the influence of abnormal data on back-end optimization, the Huber kernel function threshold adaptive adjustment strategy is introduced. The dynamic threshold is calculated based on the average visual reprojection error value of the key frames in the sliding window. Second, to effectively solve the Hessian matrix pathology problem, the Levenberg-Marquardt optimization algorithm is used to solve the objective function, which adaptively integrates the advantages of the Gaussian Newton method and the most rapid descent method. Thirdly, in order to realize the efficient fusion among multi-sensor data, they are co-calibrated and the hardware system is built. Finally, it is tested in simulation datasets and real scenarios, respectively. Compared with ORB-SLAM2 and VINS-Fusion algorithms, the root-mean-square error of our method can be reduced by up to 45.5%. In indoor small-scale scenes, the average error of our method is about 0.23 m, which is reduced by 12.3% compared with the VINS-Fusion. In indoor large-scale scenarios, our method can operate stably and obtain complete trajectories without obvious jitter and trajectory breakage. In conclusion, the overall performance of our method is better than other mainstream algorithms, with high localization accuracy and robustness, and can be widely used in various fields such as robots and UAVs to provide more accurate and robust position and localization information.