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This paper presents an improvement on the FFT-based numerical inversion of Laplace transforms. Since the inversion obtained by the FFT-based method contains large errors for the latter half of the result, only the former half is acceptable. We analyze the truncation error which is the largest part of the error, and propose the acceleration method, taking notice of the property of the complex frequency s as the differential operator in the time domain. The errors are markedly reduced by this method, and the entire result becomes acceptable.