Due to the poor coefficient of performance and low cooling capacity of thermoelectric coolers, it is necessary to use these coolers in a cascade arrangement. In this regard, two-stage coolers are very important. Considering this, in the present research, the effect of all parameters of a two-stage thermoelectric cooler on its performance was analyzed comprehensively. In this regard, the results of all parameters, including hot and cold temperatures, all geometrical parameters, as well as the thermal parameters related to the contact surface of the two stages, were analyzed analytically on COP, the dissipated heat from the cooler, and its cooling capacity. In carrying out these investigations, for the comprehensiveness of the analysis, a wide range of variation was considered for all parameters, and the optimal range of each of these parameters was reported. Then, the multi-objective optimization of the considered cooler was conducted by simultaneously considering both objective functions, including the cooling capacity and its COP, considering different values of the weighting factor. The distribution of Pareto-optimal point solutions for multi-objective optimization of the cooler was also presented which shows the optimal values of cooling capacity and COP of the cooler for different values of the weighting factor.