Organic matter (OM), iron (Fe), and zinc (Zn) in black soil are crucial to ensure high-quality production of agriculture, and hyperspectral technology is an effective approach to achieve a rapid estimation of these soil compositions. Eighty black soil samples were collected in Nehe city, Heilongjiang province, China. With indoor spectral data, the correlation between six spectral reflectance, which includes the original and five other transformed reflectance, and the contents of OM, Fe, and Zn on soil were analyzed. Then with the correlation coefficient significance test (bilateral) calculated at α  =  0.01 level to extract sensitive bands, the kernel principal component analysis (KPCA) algorithm was adopted and combined with random forest (RF) and support vector machine (SVM). The combined models were applied for quantitative inversion of soil OM, Fe, and Zn contents and compared them with the models without KPCA dimension reduction. The results show that the determination coefficients and residual prediction deviation for prediction samples of KPCA-RF model (Rp2=0.805 and RPD  =  2.329) that adopted to estimate soil OM content are higher than those of RF model (Rp2=0.681 and RPD  =  1.820), and the root-mean-square errors for prediction samples of KPCA-RF model (RMSEP  =  0.182) are lower than those of RF model (RMSEP  =  0.232). Meanwhile, the accuracy of the KPCA-RF model for estimating soil Fe and Zn contents is also higher with Rp2=0.731, 0.710, RMSEP  =  0.189, 0.003, and RPD  =  1.980, 1.905, respectively. Similarly, the accuracy of the KPCA-SVM model for estimating soil OM, Fe, and Zn contents is higher with Rp2=0.687, 0.609, and 0.585; RMSEP  =  0.230, 0.228, and 0.004; and RPD  =  1.840, 1.642, and 1.592, separately. Therefore, the machine learning models combined with KPCA are more promising in the quantitative inversion of soil composition contents and can be regarded as an effective approach.