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Aiming at improving the mapping accuracy and autonomous navigation efficiency of rescue robot in unknown environment, an improved Hector SLAM based autonomous navigation strategy is proposed, which is implemented on the Levenberg-Marquardt optimization and Bezier smooth dynamic weighted <inline-formula> <tex-math notation="LaTeX">$\text{A}^{\ast} $ </tex-math></inline-formula> algorithm. Firstly, the scan match process of Hector SLAM is performed by an improved Levenberg-Marquart (LM) method to solve the problems of non-convergence of functions and inaccurate local approximation caused by the non-singularity for solving the Hessian matrix. Secondly, the Bezier smooth dynamic weighted <inline-formula> <tex-math notation="LaTeX">$\text{A}^{\ast} $ </tex-math></inline-formula> algorithm is utilized to perform autonomous navigation based on the SLAM map. In which, the navigation target points selection is employed by the frontier exploration strategy in order to solve the search efficiency as for the increasing number of nodes in the <inline-formula> <tex-math notation="LaTeX">$\text{A}^{\ast} $ </tex-math></inline-formula> algorithm, and the accuracy of SLAM mapping declines owing to the large angle amplitude. Finally, the experiments are carried out in ROS, the results show that there is a better performance for proposed method to implement the high mapping accuracy and efficient autonomous navigation.