In this article, a dynamic clarance measurement model based on the swept frequency interferometry is formulated. The relationship among the clarance, Doppler error and light source sweeping speed is deduced. The Doppler error correction coefficient is defined to compensate for the Doppler error. The characteristics of the instantaneous frequency change of the clarance are analyzed when the sweeping speed is changed. And the applicable conditions of the Fourier transform demodulation method are obtained. The influence of the number of sparse frequency sweeping points and noise on Fourier transform demodulation is simulated and analyzed when the clarance changes in the form of a triangular wave. Then, the applicability of the method in Clearance of labyrinth measurement is analyzed. Finally, a clearance measurement system based on a fast sparse frequency-swept Clearance of labyrinth interferometry is setup and dynamic measurement experiments are carried out. Results show that the mean square error of measurement is less than 0. 2 μm when the sweeping rate is 20, 40, and 60 kHz, respectively. The clarance change frequency is 100, 500, and 1 000 Hz, respectively. And the repeatability error is less than 0. 3 μm.