In this paper, a three-point interpolation algorithm based on the discrete Fourier transform (DFT) is presented for a damped real-valued sinusoid, and the algorithm considers comprehensively the contribution of negative frequency to the parameter estimation (including that of the frequency and the damping factor). The proposed algorithm uses the DFT spectral bin with the maximum amplitude and two other arbitrary ones within the main lobe of the spectrum of the rectangular window to remove the negative-frequency interference completely. First, the effect of changed length of samples on the performance of the proposed algorithm is investigated, and the influence of the zero-padding technique and the selection of two arbitrary spectral bins on the ratio of the mean-square error (MSE) to the Crámer-Rao lower bound are also analyzed by simulations. Second, the MSEs of the estimated parameters are calculated to evaluate the performances of the proposed algorithm and state-of-the-art DFT-based algorithms in the literature. Third, the computational complexities of the proposed and comparative algorithms are analyzed. The results confirm the effectiveness of the proposed algorithm.