Linear semidefinite programming problems have received a lot of attentions because of large variety of applications. This paper deals with a smooth gradient neural network scheme for solving semidefinite programming problems. According to some properties of convex analysis and using a merit function in matrix form, a neural network model is constructed. It is shown that the proposed neural network is asymptotically stable and converges to an exact optimal solution of the semidefinite programming problem. Numerical simulations are given to show that the numerical behaviours are in good agreement with the theoretical results.