The invention provides a modular solid oxide fuel cell system. The system comprises a gas supply module, a waste heat recovery module, a galvanic pile module, a tail gas combustion module, a heat pipe module, an energy storage module, and a temperature detection and control module; a load module, the gas supply module, the waste heat recovery module and the galvanic pile module are connected in sequence; the output end of the galvanic pile module is connected with the tail gas combustion module; the heat pipe module is connected with a heat storage module and the galvanic pile module, the energy storage module is connected with the galvanic pile module, the output end of the heat pipe module is connected with the waste heat recovery module, and the waste heat recovery module exchanges heat with supplied gas of the gas supply module through a heat exchanger. The load module is responsible for tracking external load changes and transmitting load signals to the control module. According to the invention, redundant heat is stored by using the energy storage system, the temperature nonuniformity in a stack is reduced, and the service life of the SOFC is prolonged. A load tracking and electric pile sub-module in the load module and a lithium ion battery are used for carrying out quick load response, so that the stability and the reliability of an electric pile are improved.