Aiming at the low classification accuracy and efficiency of the original hyperdisk classifier, a Robust Hyperdisk Model (RHD) is proposed, where the relaxation variable is introduced based on the original hyperdisk model, and the constraints of current class samples and heterogeneous samples are considered at the same time to avoid the intersection of hyperdisks, so as to obtain a more reasonable category region estimation. Then, a Robust Nearest Neighbor Hyperdisk Classifier (RNNHDC) is proposed，which combines the RHD model with the nearest neighbor classification method. The RNNHDC only needs to calculate the distance from unknown sample points to each category RHD. And the RNNHDC has high computational efficiency and can be directly applied to multi-classification tasks. The RNNHDC has good classification efficiency. Finally, RNNHDC is applied to gearbox fault diagnosis. Experimental verification is carried out on two different gearbox datasets. The experimental results show that RNNHDC has better classification accuracy, robustness, and efficiency. The RNNHDC can be effectively used for gearbox intelligent fault diagnosis.