Abstract: When the neural network applies to optimal calculation, the ideal situation is that there is a unique equilibrium point which is globally asymptotically stable and the neural network tends to the equilibrium point at the speed of exponent. This can reduce the calculation time. The second order neural networks have faster convergence rate than the ordinary neural networks. Global exponential stability of equilibrium point for a class of second order Hopfield type neural networks is discussed by the Lyapunov method. Some criteria for global exponential stability of equilibrium point are obtained. As a special case, several new global exponential stability criteria are obtained for the corresponding Hopfield neural networks.