Heavy metal pollution in farmland soil threatens soil environmental quality. It is an important task to quickly grasp the status of heavy metal pollution in farmland soil in a region. Hyperspectral remote sensing technology has been widely used in soil heavy metal concentration monitoring. How to improve the accuracy and reliability of its estimation model is a hot topic. This study analyzed 440 soil samples from Sihe Town and the surrounding agricultural areas in Yushu City, Jilin Province. Considering the differences between different types of soils, a local regression model of heavy metal concentrations (As and Cu) was established based on projection pursuit (PP) and light gradient boosting machine (LightGBM) algorithms. Based on the estimations, a spatial distribution map of soil heavy metals in the region was drawn. The findings of this study showed that considering the differences between different soils to construct a local regression estimation model of soil heavy metal concentration improved the estimation accuracy. Specifically, the relative percent difference (RPD) of As and Cu element estimations in black soil increased the most, by 0.30 and 0.26, respectively. The regional spatial distribution map of heavy metal concentration derived from local regression showed high spatial variability. The number of characteristic bands screened by the PP method accounted for 10–13% of the total spectral bands, effectively reducing the model complexity. Compared with the traditional machine model, the LightGBM model showed better estimation ability, and the highest determination coefficients (R²) of different soil validation sets reached 0.73 (As) and 0.75 (Cu), respectively. In this study, the constructed PP–LightGBM estimation model takes into account the differences in soil types, which effectively improves the accuracy and reliability of hyperspectral image estimation of soil heavy metal concentration and provides a reference for drawing large-scale spatial distributions of heavy metals from hyperspectral images and mastering soil environmental quality.