The dynamic performance of a phasor estimation algorithm is highly expected by electric power applications. Firstly, the paper analyzes the frequency domain feature and time domain feature which a good dynamic phasor estimation algorithm should have. The frequency domain feature is that the frequency response of the algorithm near the fundamental frequency should be flat and the time domain feature is that the sample window should be as short as possible. Secondly, this paper proposes a three-quarter fundamental period least squares with band-pass filter (TQLSBF) phasor estimation algorithm which has the features mentioned above. Thirdly, the computational complexity of the proposed algorithm is analyzed and the estimation performance in various dynamic situation is simulated. The simulation results are compared with that of discrete Fourier transform phasor estimation algorithm and Taylor-Fourier Transform phasor estimation algorithm, which show that the proposed algorithm can balance the computational complex and dynamic performance efficiently.