According to the principles of energy grade recovery and cascade utilization, a novel cogeneration system including a gas turbine, a supercritical CO2 (S-CO2) recompression cycle, a steam power cycle and an organic Rankine cycle (ORC) is proposed. In particular, a part of waste heat from the supercritical CO2 recompression cycle is used to preheat the steam power cycle, and ORC uses the zeotropic mixture as working fluid. Comprehensive thermodynamic and exergoeconomic analyses are presented for the proposed cogeneration system. Parametric studies are conducted to study the effects of key system design parameters as pressure ratio of gas turbine, pressure ratio of the S-CO2 cycle, split ratio of the S-CO2 cycle, evaporation temperature of the steam power cycle, mass fraction of isopentane in the zeotropic mixture, evaporation temperature of ORC and pinch point temperature difference in the ORC evaporator on the exergy efficiency and total product unit cost. The optimum system parameters are obtained through the multi-objective optimization method based on GA (genetic algorithm) and TOPSIS (Technique for Order Preference by Similarity to Ideal Situation) decision making. The optimization results indicate that the optimum values of exergy efficiency and total product unit cost are 69.33% and 10.77$/GJ, respectively. Furthermore, the superiority of the proposed cogeneration system is verified by comparison with other seven forms of power generation systems.