This paper proposes a discrete-time neural network model to solve the convex optimization problem deduced by a positive-kernel-based support vector machine ( SVM) . First，the projection equations are constructed through the Karush-Kuhn-Tucker ( KKT) conditions and projection theory so that there exists a one-to-one correspondence between the solution of projection equations and the optimal solution of optimization problem，and then a discrete-time neural network was constructed by projection equations. Second，the obtained theoretical results indicate that the equilibrium point of the proposed neural network corresponds to the optimal solution of the optimization problem，and the proposed neural network is globally exponentially convergent. Compared with some continuous neural networks， the architecture of proposed neural network is simple， which decreases the computational complexity. Finally，some classification problems and benchmarking data sets are used in the experiment. The numeral results show the efficiency of the proposed neural network for solving the optimization problem in SVM.