As the gem trade has evolved, origin information has become a major consideration in nephrite commerce, affecting the price heavily. Accurate origin determination of nephrite is difficult due to similarities in appearances, mineral composition, major chemical components, and spectroscopy. In addition, the diversification of new nephrite deposits in the world leads to an increase in class numbers and complexity in the classification model, making it more difficult to determine the origin of nephrite. To tackle the large-class-number classification (LCNC) origin determination problem, laser inductively coupled plasma mass spectrometry (LA-ICP-MS) was utilized to detect the content of 45 major and minor elements in the nephrite sample. In addition, three different linear discriminant analysis (LDA) strategies for multi-class classification, One-off (OO), One-Versus-Rest (OVR), and One-Versus-One (OVO), were examined to evaluate the potential of a comprehensive multivariate chemometric strategy to determine the origin of nephrite samples from seven localities in three different countries (China, Russia, and South Korea) and compare their capability to improve the performance of the classification model. The results demonstrated that LA-ICP-MS coupled with multi-strategy LDA can be used to determine the origin of nephrite with a high level of accuracy. The One-off LDA model achieved classification accuracies of 95.8% and 93.3% in original classification and leave-one-out cross-validation (LOOCV), respectively. Nonetheless, this method has poor capabilities in solving large-number class classification problems, and the data of the classes in discriminant models overlap. OVR-LDA and OVO-LDA were used to handle multiclass problems by transforming multiple classes into a set of binary cases. These two strategies both were demonstrated to be capable of differentiating the origin and achieved improved performance in dealing with the multi-class problem. Most importantly, we critically analyze the performance of the three LDA strategies in classification models and reveal their appealing properties, matters that need attention, and application prospects. We also investigate the element combinations that contribute greatly to classification functions and discuss the rationale of nephrite origin performance in the origin determination model from a geological perspective.