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Aiming at the problem that the traditional path following control method of mobile robot requires manual tuning parameters and lacks of self-optimization ability, a path following control method based on heuristic dynamic programming (HDP) was proposed. Firstly, the error state equation of the path following system was established based on the structure of tracked robot system. Secondly, a path following controller based on HDP algorithm was proposed. The return function was designed by synthesizing the error performance index and the following stability index. A multi-layer feedforward neural network was used to establish the actuator and evaluation modules, and the online optimization rules of network parameters were derived. Thirdly, the path following performance of HDP method was verified by numerical simulation and system test. The experimental results showed that the controller based on the HDP algorithm of the mean absolute error was 0.04m and the root mean square error was 0.06m when following a straight line, 0.01m and 0.06m when following a obtuse angle steering curve, and 0.03m and 0.09m when following an acute angle steering curve, and the method based on HDP can obtain high precision control effect without repeated debugging control parameters, and it improved the environmental adaptability and autonomous optimization ability of the path following control method for mobile robots.