An error model of phase discrimination based on spectral analysis is deduced to reduce the phase discrimination error for a phase-shift laser range finder, and the Hilbert transform is induced to data pre-processing to eliminate the estimation bias of phase difference. The bias and deviation of conventional spectrum analysis phase discrimination are analyzed. The analysis shows that the bias is influenced by initial phases and it can not be ignored in fast and precision measurement.This paper proposes an unbiased improvement method. The method uses a window function to design a simple Hilbert transformer to convert the objective of Discrete Fourier Transform into an analytic signal. Then the nearly unbiased phase difference measurement is achieved by spectral analysis only in increasing four addition and two shift operations. Simulation and experimental results indicate that the mean phase is the same as the real phase difference. When the signal to noise ratio is 40 dB, the measurement accuracy for the high speed phase discriminaton is 0.1°. When the modulation frequency is 100 MHz, the distance measurement accuracy is 0.4 mm. Results show that the Hilbert transform can help spectral analysis realize high accuracy phase difference measuring and the method can be applied to fast phase-shift laser range finders.