This study proposed a technique for identifying the authenticity of geographic indication mutton based on mineral element fingerprint combined with one-class modeling strategy. The results showed that the contents of mineral elements in the meat of Yanchi Tan sheep, Balikun Kazak sheep and Sunit sheep under the protection of geographical indication had fingerprint characteristics. In the one-class modeling strategy, only real sample sets were collected for modeling to identify the real samples from a variety of fraud samples. The soft independent modeling of class analogy (SIMCA) model based on each of the geographical indication mutton samples had excellent performance, with an identification accuracy of 100% for the test samples. Therefore, mineral element fingerprint combined with one-class modeling has a wide application prospect in the field of authenticity identification of geographical indication mutton.