Generalized Eigenvalue Proximal Support Vector Machine (GEPSVM) is an extremely fast and simple algorithm for generating linear and nonlinear classifiers. Kernel functions are essential in fitting GEPSVM. Usually a single kernel is used by most researchers in their studies, but the real world applications may require a combination of multiple kernel functions. There are two kind of kernels which known as global and local kernels. Global kernel functions have good generalization ability, but low learning ability. Local kernel functions have good learning ability with weak generalization. The presented approach constructs a mixed kernel function with better performance by fully combining local kernel function for strong learning ability and global kernel function for strong generalization. The Backtracking Search Algorithm (BSA) is used for determining the best value of the weight parameter between the two kernels. To evaluate the performance of the proposed approach, we applied it to public datasets from UCI repository.