Hyperspectral technology has unique advantages in the inversion of soil heavy metal content. Still, there is a large amount of redundant information in the hyperspectral data, and corresponding methods are needed to reduce the influence of redundant information on the inversion accuracy to realize the accurate prediction of soil Zn content. In this study, we used the soil Zn content and hyperspectral data collected from the farmland of Mojiang Hani Autonomous County, Yunnan Province, as the data source, and Savitzky-Golay smoothed the acquired hyperspectral data, and then four different mathematical transformations, R′，(1／R)′，（）′ and (logR)′ were used to process the spectra. Five indexes are constructed, namely normalized index (NDI), difference index (DI), ratio index (RI), sum index (SI), and inverse difference index (IDI). The spectral index with the largest absolute value of the correlation coefficient with the soil Zn content was selected as the input to the model and combined with the partial least squares method (PLSR) and multiple regression (MLR) to establish an optimal inversion model for soil Zn content. The results show that (1) the optimized spectral indices exhibit high correlations with soil zinc content under various mathematical transformations. These indices effectively enhance the sensitivity of spectral measurements to variations in zinc levels, with correlation coefficients achieving absolute values of 0.7 or higher. (2) The best prediction model (1/R)′ PLSR based on the optimized spectral index has a validation set of R² of 0.77, RMSE of 5.07 mg·kg^-1, and RPD of 2.09. Compared with the MLR model with the same variable, the R² increased by 0.04, the RMSE decreased by 0.47, and the RPD increased by 0.18, which has better predictive ability and can be used as an optimal estimation model for soil Zn content in the study area. (3) the spatial distribution map of soil Zn content in the study area was drawn based on the optimal estimation model combined with the spatial interpolation method. It can be seen that the spatial distribution of soil Zn content is higher in the middle of the map and decreases with the increase of terrain elevation. It is feasible to estimate soil Zn content based on an optimized spectral index combined with the PLSR modeling method, which can provide a reference for estimating Zn content in farmland soil.