Aiming at the problems of harmonic crosstalk and small dynamic measurement range in traditional frequency modulation continuous wave laser interferometer displacement sensors， a three-channel displacement measurement system with three independent Fabry-Perot interferometer detection optical paths is developed. The system includes three chips， and the operation speed can be improved by using multi-chip processing. The simultaneous measurement of each chip is controlled by the equal length of the signal line and software， which can solve the problem of non-synchronization of the independent channel measurement. The experimental results show that the synchronization measurement error of each channel for a moving target with a velocity of 1 mm/s is only 0.46 nm， the standard deviation of the displacement measurement error of a 600 mm stroke is less than 3 nm， and the linear fitting coefficient is above 0.99997， indicating that this system can achieve the displacement measurement of three-dimensional moving targets.