Due to the high-temperature operation of solid oxide fuel cell, recovering its exhaust waste heat is worthwhile. The supercritical CO2 cycle features low compression power consumption and high thermal efficiency, making it a promising power cycle. Therefore, this paper adopts the supercritical CO2 recompression cycle as the bottom cycle, combined with solid oxide fuel cell to form a joint system, further improving energy utilization. Given the long temperature response time of the solid oxide fuel cell and the variability of its exhaust waste heat with load changes, this paper innovatively proposes establishing an integrated dynamic model of the joint system, instead of directly providing heat source flow and temperature changes as in traditional research, to more accurately study the dynamic response of the cycle during solid oxide fuel cell startup and load variations. Based on this, a control strategy utilizing inventory control is proposed, and the feasibility of the control effect is verified. The research results indicate that the uncontrolled cycle may lead to safety issues with a significant increase in turbine inlet temperature when solid oxide fuel cell load increases. Under the control strategy, the turbine inlet temperature and main compressor inlet temperature are rapidly stabilized at the target values. The controlled cycle achieves higher efficiency compared to the uncontrolled cycle, particularly prominent during solid oxide fuel cell load reduction, with an efficiency increase of approximately 5.23%.