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In this paper, a new algorithm, namely, a reduced Hessian sequential quadratic programming (SQP) method, for solving electromagnetic inverse problems is proposed. The electromagnetic inverse problem is considered to be a constrained nonlinear programming. The reduced Hessian SQP method finds the solution of this constrained nonlinear programming by solving a sequential of quadratic programming subproblems. The reduced Hessian scheme is applied to reduce the requirement of computational memory of the basic SQP method for large inverse problems. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method, and some comparisons show that the proposed method has a better convergence and a faster speed than the previous methods.