In this paper, we propose a Novel Convex Polyhedron classifier (NCPC) based on the geometric concept convex hull. NCPC is basically a linear piecewise classifier (LPC). It partitions linearly non-separable data into various linearly separable subsets. For each of these subset of data, a linear hyperplane is used to classify them. We evaluate the performance of this classifier by combining it with two feature selection methods (Chi- squared and Anova F-value). Using two datasets, the results indicate that our proposed classifier outperforms other LPC- based classifiers.