A smoothing-type algorithm for solving the generalized support vector machines(SVMs) is proposed. Based on the KKT system of the dual optimization model for SVMs, a new class of smoothing functions is proposed, and the KKT system is reformulated as a system of parameterized smooth equations and solved by using the smoothing type algorithm. Under some reasonable conditions, the proposed algorithm is shown to be globally convergent and locally superlinearly convergent. Numerical examples show that the proposed algorithm is promising and has a bright future of applications.