Based on mathematical modelling and numerical simulations, a control strategy for a Molten Carbonate Fuel Cell Hybrid System (MCFC-HS) is presented. Adequate maps of performances with three independent parameters are shown. The independent parameters are as follows: stack current, fuel mass flow and compressor outlet pressure. Those parameters can be controlled by external load, fuel valve and turbine-compressor shaft speed, respectively. The control system is purposed to meet many constraints: e.g. stack temperature, steam-to-carbon ratio, compressor surge limitation, etc. The aim is to achieve maximum efficiency of power generated within these constraints. Governing equations of MCFC-HS modelling are given. An operational line of the MCFC-GT system is presented which fulfils several constraints (temperature difference, cell temperature, etc.) The system is able to achieve efficiency of more than 62% even in part-load operation.