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A fast algorithm for finding the frequency-domain solutions of electromagnetic field computation using time-domain finite-element method (FEM) is presented. Base solutions, which are time-domain solutions when the excitations are substituted by step functions, are computed first using time-stepping FEM in time domain. Then, based on these base solutions in time domain, all solutions in frequency domain at different operating frequencies can be easily and quickly obtained by simple addition and subtraction operations. It can be seen, from a numerical experiment on the performance analysis of a magnetic-resonant wireless power transfer system, that the computing time of the proposed time-domain method is less than 5% of that required if conventional frequency-domain method is used. The proposed method can be generalized and extended to any linear systems.