Radial Basis Function (RBF) has been widely used in different fields, due to its fast learning and interpretability of its solution. One problem of classical RBF is that it suffers from curse of dimensionality that the number of basis functions will explode with the increase of dimensions in the dataset. This explosion usually impairs the usefulness and interpretability of RBF, especially in medical applications, where the dimensions of dataset are high and the explanations of solutions are important. In this paper, we propose a generalized RBF (GRBF) model to reduce the number of basis functions and thus alleviate curse of dimensionality. An EM-based training algorithm is also introduced, which uses fewer parameters compared to some classical supervised learning methods. This will make the learning process simpler and more convenient in practice. Moreover, GRBF trained by the new algorithm has an apparent statistical meaning. Experimental results show potentials for real-life applications.