In this paper, a new nonparametric Thevenin equivalent parameters (TEPs) estimation method is proposed by using local measurements. It is achieved by considering the TEPs estimation issue as a classical optimized denoising problem. The noise characteristics are analyzed through stochastic simulation experiments. Then, a nonparametric regression algorithm named taut-string-multiresolution is employed to obtain the optimized TEPs estimation results. Compared with the classic Total Variation (TV) based denoising model, the proposed estimation method has relatively stable performance in different operation conditions, without the need for predetermination of any parameters. The effectiveness of the proposed TEPs estimation method is verified by an ideal two-bus equivalent system under two different operation scenarios.