Setting reasonable circuit parameters is an important way to improve the quality of inverters, including waveform quality and power loss. In this paper, a circuit system of line voltage cascaded quasi-Z-source inverter (LVC-qZSI) is built. On this basis, the double frequency voltage ripple ratio and power loss ratio are selected as optimization targets to establish a multi-objective optimization model of LVC-qZSI parameters. To simplify the calculation, an integration optimization strategy of LVC-qZSI parameters based on GRA-FA is proposed. Where, the grey relation analysis (GRA) is used to simplify the multi-objective optimization model. In GRA, the main influence factors are selected as optimization variables by considering the preference coefficient. Then, firefly algorithm (FA) is used to obtain the optimal solution of the multi-objective optimization model. In FA, the weights of objective functions are assigned based on the principle of information entropy. The analysis results are verified by simulation. Research results indicate that the optimization strategy can effectively reduce the double frequency voltage ripple ratio and power loss ratio. Therefore, the strategy proposed in this paper has a superior ability to optimize the parameters of LVC-qZSI, which is of great significance to the initial values setting.