Summary: Sinusoidal representation has been widely applied to speech modification, low bit rate speech and audio coding. Usually, speech signal is analyzed and synthesized using the overlap-add algorithm or the peak-picking algorithm. But the overlap-add algorithm is well known for high computational complexity and the peak-picking algorithm cannot track the transient and syllabic variation well. In this letter, both algorithms are applied to speech analysis/synthesis. Peaks are picked in the curve of power spectral density for speech signal; the frequencies corresponding to these peaks are arranged according to the descending orders of their corresponding power spectral densities. These frequencies are regarded as the candidate frequencies to determine the corresponding amplitudes and initial phases according to the least mean square error criterion. The summation of the extracted sinusoidal components is used to successively approach the original speech signal. The results show that the proposed algorithm can track the transient and syllabic variation and can attain the good synthesized speech signal with low computational complexity.