To rapidly obtain the transient magnetic field variations and losses of electrical equipment, studying fast calculation methods for time-harmonic magnetic fields is of great significance. By combining time-harmonic field simulation with the proper orthogonal decomposition （POD) and surrogate modeling approach, rapid calculation of magnetic field distribution and losses under high-order harmonics is achieved. To improve the accuracy of the calculation method, an improved radial basis function （RBF) response surface model capable of automatically selecting the order of linear polynomials was introduced. Compared to the RBF response surface model incorporating linear polynomials, this improved model further enhances its engineering applicability and computational accuracy. To validate the effectiveness of the proposed method, full-order simulation and reduced-order analysis of the time-harmonic field are first conducted on the TEAM7 problem, demonstrating the accuracy of the proposed approach. Additionally, the proposed method is compared with traditional RBF response surface methods and RBF methods incorporating linear polynomials, with results showing a significant improvement in accuracy. Finally, the POD and improved RBF response surface method with linear polynomials are combined to perform reduced-order calculations for the time-harmonic magnetic field of a transformer. The results indicate that the reduced-order calculation offers a significant advantage in computational time while maintaining relatively small errors.