The thermal efficiency of the Maisotsenko gas turbine cycle (MGTC) needs to be further improved, and its economic feasibility has not been properly evaluated. Unlike the two-stage MGTC with aftercooling and regenerative processes, a three-stage MGTC system (IMGTC) layout with coupling of intercooling process was constructed by fully considering the reuse of cooling water and energy recovery. The effects of pressure ratio (R_c), air saturator degree of humidification (H_ASD) and combustor outlet temperature (T_CO) on thermal efficiency, saturation amount of water in saturator, equivalent carbon dioxide emissions (E_EC), and levelized cost of electricity (C_LOE) were studied. Finally, a multi-objective optimization of the system was carried out on the ISIGHT platform to select the best parameter combination. The results indicate that the intercooler and its energy efficiency improvement in IMGTC can adjust and effectively reduce the saturation amount of water in the saturator. The minimum saturation amount of water in the IMGTC system is only 57.55% of that in the no-intercooling mode. The multi-objective optimization shows that when using the optimal parameter combination, the thermal efficiency of IMGTC reaches 49.89%, while E_EC and C_LOE are only 5.496 kg/s and 0.059 5 USD/kWh, respectively. This research confirms the significant advantages of IMGTC over MGTC in terms of thermodynamic performance and economic feasibility.