SOFC-Engine hybrid power system is a promising energy conversion technology with high efficiency. However, its dynamic behaviors are still unclear. Herein, the dynamic modeling of this hybrid system is performed. Besides, the control strategies of hydrogen addition and power distribution are further investigated to enhance the system performance. The results show that the relatively slow dynamics of the SOFC component is dominating in the hybrid system. The reason is mainly attributed to that the autonomy of the engine with fast dynamics is partly restricted without hydrogen addition. When hydrogen is fed to the engine as a part of inlet fuel by metal hydride and waste heat recovery unit, the dynamics of the hybrid system can be improved. Moreover, the efficiency can also be improved to 67.6% with the hydrogen addition ratio χ = 2.0. After that, the control strategy for power distribution is proposed to achieve the optimal overall performance for the hybrid system. The SOFC provides most of the output power as a stable power baseline and the engine copes with the dynamic part. In such a strategy, the hybrid system enables to respond to the change of power load within 1 s and to achieve the overall energy conversion efficiency up to 75%, which is promising for the vehicle applications. In brief, this work can provide an insight into the dynamic behaviors of the SOFC-Engine hybrid energy conversion system to obtain the feasible operation strategy for its vehicle applications. © 2020 Elsevier B.V.