The frequency-modulated continuous wave laser interferometry is widely used in the field of precision measurement. Aiming at its high-precision displacement demodulation problem, this paper applies the centroid method to the demodulation of its beat signal, proposes a phase demodulation algorithm based on the centroid peak-seeking method, and carries out experiments and analysis. Based on the smooth filtering and peak clipping of the intercepted beat signal, the proposed algorithm obtains the centroid of the beat signal through the centroid coordinate formula. The abscissa of the centroid is the peak position. Finally, the phase discrimination algorithm demodulates the displacement. In the simulation, the SNR is set to 15 dB, the phase error of the algorithm is 0.016 rad, and the displacement error is 2.04 nm. A frequency-modulated continuous wave laser interference displacement measurement system was built for experimental verification. The experimental results show that when the fixed distance is 44 mm, the standard deviation of random displacement error is 2.18 nm. Compared with the conventional zero crossing detection method, the measurement error of the algorithm is reduced by 49%, the resolution is improved, and the algorithm has broad application prospects.