Laser frequency scanning interference technology has become a research hotspot due to its high precision and strong anti-interference capability and other advantages. The nonlinear problem of laser frequency modulation has always been a key factor affecting the accuracy of the measurement system. The most direct result of the nonlinearity of frequency modulation is that the spectrum of the beat signal is severely broadened, resulting in a decrease in the ranging accuracy. In order to solve this problem, this paper proposes a nonlinear correction method based on the Lomb-Scargle algorithm, and builds a laser frequency sweep interferometry system with an auxiliary interferometer. The phase is extracted by performing Hilbert transform on the auxiliary path beat signal, thereby generating a new time series based on the extracted phase information. The generated time series carries the phase change information of the auxiliary path beat signal, and it is combined with the Lomb-Scargle algorithm to perform the nonlinear correction of the measurement system and the frequency calculation of the beat signal simultaneously. As a verification, the targets in the range of 0.5–1.3 m are measured with a maximum error of 14 μm. The traditional frequency sampling method is limited by the Nyquist sampling theorem, and the laser emission and reception need to travel a round-trip distance, which means that the frequency sampling method must meet the requirement that the distance of the measured target cannot exceed a quarter of the optical path difference of the auxiliary interferometer. Therefore, the range of distance measurement is limited when the optical path difference of the auxiliary interferometer is constant. Different from the correction principle of the traditional frequency sampling method, the correction method proposed in this paper does not use the beat signal of the auxiliary path to resample the measurement path, so there is no need to satisfy the condition that the optical path difference of the auxiliary interferometer is greater than four times the measuring distance. Therefore, in the case of a certain optical path difference of the auxiliary interferometer, it can provide a way to increase the ranging range of the system.