The Chinese Fusion Engineering Testing Reactor (CFETR) power conversion system with Supercritical CO2 (SCO2) Brayton cycle is designed, analyzed and optimized at present. Considering the pulse operation of the reactor, a heat storage loop with high temperature molten salt and low temperature concrete is introduced. Based on the parameters of the first cooling loop, the CFETR power conversion loop is designed and studied. A new SCO2 Brayton cycle for the CFETR dual heat sources, blanket and divertor, is developed and optimized by genetic algorithm. Compared to other simple and recompression cycles, it is shown that the new SCO2 Brayton cycle has the maximum thermal efficiency with simplicity. The exergy analyses are carried out and show that the exergy destruction rates of turbine and heat exchangers between different loops are the largest due to the large turbine power and the large temperature difference. The exergoeconomic analyses show that fusion reactor accounts for the main cost, which is the key to the economy of fusion power generation. The following sensitivity analyses show that the hot molten salt temperature has a major influence on the system performance. Finally, several multi-criteria optimization algorithms are introduced to simultaneously optimize the three fitness functions, the cycle thermal efficiency, the system exergy efficiency and the total system product unit cost. It is found that the maximum thermal efficiency, the maximum exergy efficiency and the lowest total system product unit cost can be obtained almost simultaneously for the new CFETR power conversion system, and the optimal operation scheme is given in the end.