The k sub-convex-hull classifier is widely used in practical problems. But with the increase of the dimension of the problem, these convex distances calculated by the method are very close to or even equal, which seriously affectes the performance of classification. To resolve the above problems, a relative k sub-convex-hull classifier based on feature selection (FRCH) is designed in this paper. Firstly, the definition of the relative k sub-convex-hull is introduced according to the shortcomings of absolutely convex hull distance. Then, the feature selection is carried out by using the discriminant regularization technique in the k neighborhood. Moreover, the feature selection method is embedded in the optimization model on the relative k convex hull. Through these efforts, an adaptive feature subset in different categories for each test sample can be extracted, and a valid relative k sub-convex-hull distance can be obtained. Experimental results show that our FRCH not only can make the feature selection practicable, but also significantly improves the classification performance of the k sub-convex-hull classifier.