This paper describes a fast and effective algorithm for refining the parameter estimates of multicomponent third-order polynomial phase signals (PPSs). The efficiency of the proposed algorithm is accompanied by lower signal-to-noise ratio (SNR) threshold, and computational complexity. A two-step procedure is used to estimate the parameters of multicomponent third-order PPSs. In the first step, an initial estimate for the phase parameters can be obtained by using fast Fourier transformation (FFT), k-means algorithm and three time positions. In the second step, these initial estimates are refined by a simple moving average filter and singular value decomposition (SVD). The SNR threshold of the proposed algorithm is lower than those of the non-linear least square (NLS) method and the estimation refinement method even though it uses a simple moving average filter. In addition, the proposed method is characterized by significantly lower complexity than computationally intensive NLS methods. Simulations confirm the effectiveness of the proposed method.