Due to the high computational complexity of kernel matrixes, traditional kernel-based methods can not satisfy the requirement of large-scale data classification. To solve this problem, a fast convex hull classifier based on random projection(FCHC-RP) is proposed. In the FCHC-RP, the samples in the original space are projected into several two-dimensional subspaces, and then the data in subspaces are mapped into the kernel space. Then, the convex hull candidate set is computed according to the geometric characteristics of data distribution in the kernel space. Based on the definition of the convex hull, the convex hull vectors in the kernel space are computed. Finally, the support vector machine is trained by the convex hull vectors and their weights. In addition, the FCHC-RP is also suitable for imbalanced classification problems. The FCHC-RP adopts classifier parameters according to the degree of class imbalance between two classes, so that the size of convex hull sets belonging to two class samples is similar. Thus, the training data in two classes are comparative. Theoretical analysis and experimental results verify the advantages of the FCHC-RP in classification performance and training time.