In this paper, a method to generalize previously proposed Chebyshev Kernel function is presented for Support Vector Classification in order to obtain more robust and higher classification accuracy. By introducing the generalized Chebyshev polynomials for vector inputs, we increase the performance of this kernel function. The simulation results show that the proposed generalized Chebyshev Kernel has better performance than the previously proposed kernel for Support Vector Classification. Early simulation results show that the proposed kernel function yields the best classification results for a Breast Cancer dataset.