In order to reduce the cost of single-phase multi-input/output transformer, the relationship between total loss and total cost is balanced by taking the lowest total cost and total loss of transformer as the objective function, and the sum of total cost and total loss with a weight ratio of 8:2 as the total target parameters, the optimal transformer design scheme with the lowest total target parameters is designed by using a multi-objective optimization algorithm based on genetic algorithm and adding non-dominant sorting, and the optimal transformer design scheme with the lowest total target parameters is designed by optimizing the core width, magnetic flux density and winding wire diameter of the transformer. In order to determine the optimization results of the algorithm, this paper compares the design parameters of the transformer before optimization, and the results show that the total cost is reduced by 10.717 RMB and the total loss is reduced by 8.16W, and the optimized design parameters effectively reduce the total cost and total loss of the transformer. The finite element analysis COMSOL software was used to establish a simulation model of the electromagnetic-magnetic-thermal field coupling of a single-phase multi-winding transformer, and the accuracy of the design was verified by the bidirectional coupling calculation. By observing the voltage, current, and temperature field distribution of the transformer, the rationality of the optimal design of the transformer is verified.