Soil nutrients, including soil available potassium (SAK), soil available phosphorous (SAP), and soil organic matter (SOM), play an important role in farmland soil productivity, food security, and agricultural management. Spectroscopic analysis has proven to be a rapid, nondestructive, and effective technique for predicting soil properties in general and potassium, phosphorous, and organic matter in particular. However, the successful estimation of soil nutrient content by visible and near-infrared (Vis-NIR) reflectance spectroscopy depends on proper calibration methods (including preprocessing transformation methods and multivariate methods for regression analysis) and the selection of appropriate variable selection techniques. In this study, raw spectrum and 13 preprocessing transformations combined with 2 variable selection methods (competitive adaptive reweighted sampling (CARS) and the successive projections algorithm (SPA)) and 2 regression algorithms (support vector machine (SVM) and partial least squares regression (PLSR)), for a total of 56 calibration methods, were investigated for modeling and predicting the above three soil nutrients using hyperspectral Vis-NIR data (400–2450 nm). The results show that first-order derivatives based on logarithmic and inverse transformations (FD-LGRs) can provide better predictions of soil available potassium and phosphorous, and the best form of soil organic matter transformation is SG+MSC. CARS was superior to the SPA in selecting effective variables, and the PLSR model outperformed the SVM models. The best estimation accuracies (R2, RMSE) for soil available potassium, phosphorous, and organic matter were 0.7532, 32.3090 mg/kg; 0.7440, 6.6910 mg/kg; and 0.9009, 3.2103 g/kg, respectively, and their corresponding calibration methods were (FD-LGR)/SPA/PLSR, (FD-LGR)/SPA/PLSR, and SG+MSC/CARS/SVM, respectively. Overall, for the prediction of the soil nutrient content, organic matter was superior to available phosphorous, followed by available potassium. It was concluded that the application of hyperspectral images (Vis-NIR data) was an efficient method for mapping and monitoring soil nutrients at the regional scale, thus contributing to the development of precision agriculture.