In this paper, we study a gradient-based neural network method for solving strictly convex quadratic programming (SCQP) problems. By converting the SCQP problem into a system of ordinary differential equation (ODE), we are able to show that the solution trajectory of this ODE tends to the set of stationary points of the original optimization problem. It is shown that the proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem. It is also found that a larger scaling factor leads to a better convergence rate of the trajectory. The simulation results also show that the proposed neural network is feasible and efficient. The simulation results are very attractive.