A combined system including a solid oxide fuel cell (SOFC) and an internal combustion engine (ICE) is proposed in this paper. First, a 0-D model of SOFC and a 1-D model of ICE are built as agent models. Second, parameter analysis of the system is conducted based on SOFC and ICE models. Results show that the number of cells, current density, and fuel utilization can influence SOFC and ICE. Moreover, a deep neural network is applied as a data-driven model to conduct optimized calculations efficiently, as achieved by the particle swarm optimization algorithm in this paper. The results demonstrate that the optimal system efficiency of 51.8% can be achieved from a 22.4%/77.6% SOFC-ICE power split at 6 000 kW power output. Furthermore, promising improvements in efficiency of 5.1% are achieved compared to the original engine. Finally, a simple economic analysis model, which shows that the payback period of the optimal system is 8.41 years, is proposed in this paper.