A classifier design method based on conformal geometric algebra and quadratic programming is proposed. From a new point of view, the probability and simplicity of using the conformal geometric algebra to design optimal separation hyersphere is discussed. A geometrical representation of separating hypersphere is firstly introduced based on conformal geometric algebra, by which the two-class optimal separation hyersphere separation problem may be transformed into the training problem based on quadratic programming. According to this, the design and training of multi-class classifier are analyzed. The algorithm not only keeps the advantages of maximizing the margin, generalizing the optimal separating hyperplane to optimal separating hypersphere, but also simplifies computational complexity. Simulation results show that the algorithm is compact and explicit, and the integrations of algorithm have an important significance in the improvement of efficiency.