Aiming at improving the accuracy of parameter estimation, this paper proposes an iterative algorithm for one/multiple damped real-valued sinusoids. Firstly, an initial three-point interpolation estimator is established for one damped real-valued sinusoid by completely removing the negative-frequency interference. Secondly, to reduce the effect of the theoretical frequency on the estimation accuracy, a fine estimator is further presented. Finally, based on the fine estimator, parameters including the frequency, the damping factor, the amplitude, the phase can be further iteratively estimated from multiple damped real-valued sinusoids. In the numerical analysis, the root of mean square error (RMSE) returned by the proposed algorithm is compared with RMSEs returned by other state-of-the-art algorithms, as well as the square root of the Cramér-Rao lower bound (CRLB). Results show that the RMSE returned by the proposed algorithm is much closer to the square root of the CRLB, which implies that the proposed algorithm can effectively achieve high-accuracy parameter estimation from one/multiple damped real-valued sinusoids.