The laser frequency scanning interferometry, as a non-contact method, has non-ranging blind zone and achieves multi-target testing in a single measurement. The beat frequency of target can be extracted by Fourier transform, and then the distance can be solved. However, due to the limitation of laser frequency modulation bandwidth, the resolution of target obtained by Fourier transform is limited to the inherent resolution. In order to solve this problem, in this paper we propose to use the estimating signal parameter via rotational invariance technique (ESPRIT) to perform spectrum analysis on the measured signal. In the experiment, the resampling method is adopted to correct the non-linearity of the measured signal beat frequency, and then the ESPRIT algorithm is used to obtain the target distance. The results show that the Fourier transform algorithm cannot distinguish the target signal from the frequencies of adjacent target, but the ESPRIT algorithm can do. The thickness of the measured target is 2.08 mm. This provides ideas for measuring, such as damage point in the proximity of the fiber, height of thin step, or small hole.