Abstract: For small sample size problem in high-dimensional space, conventional classifiers with reject option based on statistical model could not construct appropriate covering decision boundary on data distribution. In this case, a novel adaptive Minimum Spanning Tree (MST) covering model based classifier with reject option is proposed in this paper according to the data distribution in high-dimensional space. The algorithm describes the target class using MST with the assumption that the edges of the graph are also basic elements of the classifier which offers additional virtual training data for a better coverage. By this model, similar samples from the same class are divided into a connected geometric coverage area, and similar samples from different classes are divided into different geometric coverage areas. Furthermore, in order to reduce the degradation of the rejection performance due to the existence of unreasonable additional virtual training data, an adjustable coverage radius strategy is presented in coverage construction. Then the test pattern of non-training classes could be rejected by the coverage decision boundary, and if a pattern is accepted in the cross coverage area, the recognition result is decided by the data fields model. Experiments show that the method is valid and efficient.