In this paper, on the basis of the traditional interpolation algorithm using FFT, an algorithm which can improve the accuracy of interpolation is proposed. The algorithm here overlap and cut the subsequences, then discard the samples with great error at both ends of interpolated sequence and reconstruct the relatively accurate samples. In this way, the accuracy of interpolation can be significantly improved. Experimental results show that, compared with the interpolation algorithm proposed by Prasad, in case of computational amount increase by 3.1%, the normalized mean square error corresponding to different subsequence length decrease to 1/19 of its original in average; in case of computational amount increase by twice, the normalized mean square error corresponding to different subsequence length decrease to 1/75 of its original in average.