Three sequential optimization methods, sequential least square method, sequential Kriging method, and sequential linear Bayesian method, are presented for the optimization design of electromagnetic device. Sequential optimization method (SOM) is composed of coarse optimization process and fine optimization process. The main purpose of the former is to reduce the design space; while the target of the latter is to update the optimal design parameters. To illustrate the performance of the proposed methods, an analytic test function and the TEAM Workshop Problem 22 are investigated. Experimental results of test function demonstrate that SOM can obtain satisfactory solutions; and practical application illustrates that the number of finite element sample points is less than 1/10 compared with that by direct optimization method, while the optimal results are even better than that by direct optimization method.