As society advances and science and technology progress continuously, the requirements for electrical equipment have become increasingly stringent. Among these challenges, the optimization design of electromagnetic devices poses a complex multi-objective optimization problem due to the existence of coupled physical fields and the involvement of multiple conflicting objectives. Evolutionary-based optimization algorithms are widely employed to address such issues because of their practicality and effectiveness. However, many algorithms are prone to falling into local optima and exhibit poor stability when dealing with complex, high-dimensional, nonlinear mathematical programming problems. To address these issues, an improved multi-objective grey wolf optimization algorithm is proposed. In the improved algorithm, a good point set strategy is utilized in the population initialization; a nonlinear convergence factor is adopted to balance the algorithm’s optimization speed and accuracy; the Levy flight strategy is introduced to effectively utilize the search space, and the population updating mechanism in the beluga whale algorithm’s whale-fall behavior is introduced to further enhance the global search ability. The performance of the proposed algorithm is verified by means of the ZDT series test functions and is applied to the optimal design of a typical electromagnetic device. The numerical results manifest its accuracy and effectiveness.