A new gas turbine-fuel cell Hybrid Cycle is proposed. The fuel cell advantageously operates close or under atmospheric pressure and is fully integrated with the gas turbine that is based on an Inverted Brayton-Joule Cycle. The idea of the invention is to capitalize on the intrinsic oxygen-nitrogen separation characteristic of the fuel cell electrolyte by sending to the Inverted Brayton-Joule Cycle only the anodic flow, which is the one free of nitrogen. In this way the flow that expands in the turbine consists only in steam and carbon dioxide. After the expansion the steam can be easily condensed, separated and pumped up. Therefore the compressor has mainly only to compress the separated carbon dioxide. This effect generates a substantial advantage in term of efficiency and enables separating the carbon dioxide. The new proposed Hybrid Cycle enables to: substantially increase the system efficiency compared to the known gas turbine-fuel cell Hybrid Cycle, maintain the fuel cell operating under or close to atmospheric pressure and separate the carbon dioxide.