Strong restrictions on emissions from marine power plants (particularly $SO_x$, $NO_x$) will probably be adopted in the near future. In this paper, a combined solid oxide fuel cell (SOFC) and gas turbine fuelled by natural gas is proposed as an attractive option to limit the environmental impact of the marine sector. It includes a study of a heat-recovery system for 18 MW SOFC fuelled by natural gas, to provide the electric power demand onboard commercial vessels. Feasible heat-recovery systems are investigated, taking into account different operating conditions of the combined system. Two types of SOFC are considered, tubular and planar SOFCs, operated with either natural gas or hydrogen fuels. This paper includes a detailed thermodynamic analysis for the combined system. Mass and energy balances are performed, not only for the whole plant but also for each individual component, in order to evaluate the thermal efficiency of the combined cycle. In addition, the effect of using natural gas as a fuel on the fuel cell voltage and performance is investigated. It is found that a high overall efficiency approaching 70% may be achieved with an optimum configuration using SOFC system under pressure. The hybrid system would also reduce emissions, fuel consumption, and improve the total system efficiency.