Frequency-modulated continuous-wave (FMCW) laser ranging technology is an important development direction of light detection and ranging (LiDAR) for the future. It has the advantages of high ranging accuracy, high resolution, wide range, and no ranging blind zone. A distributed feedback laser can be used as a high-quality light source in FMCW laser ranging systems because of its wide frequency modulation range, simple frequency modulation mode, and small package. Aiming at the nonlinear problem of the laser in the frequency modulation process, we present a novel, to our knowledge, predistortion algorithm based on interpolation linear fitting to enhance the linearity of the FMCW laser for LiDAR systems. The sweeping frequency curve of the laser is obtained using the Hilbert transform, and then the sweeping frequency curve is segmented and linearly fitted to calculate the interpolated driving current signals corresponding to linear frequency changes. Using this method, we achieved a nonlinearity error lower than 1e-7 for the swept-frequency signal and demonstrated that the ranging error is less than ±5c m at a distance of 100 m in the FMCW system. In addition, we also demonstrated a 3D static object point cloud with high imaging quality. Compared with the iterative predistortion algorithm based on the function fitting, this method avoids fitting errors at the inflection points of the triangular swept-frequency signal and the complexity of multiple iterative calculations. It enables rapid generation of pre-distorted swept-frequency signals, making it particularly suitable for real-time applications of automotive LiDAR systems.