Hopfield proposed two types of neural networks; Discrete Hopfield Network(DHN) and Continuous Hopfield Network(CHN). Those have been used for solving the famous traveling salesman problem in a sense of optimization. DHN, a stochastic model is simple to implement and fast in computing, but it uses binary value for states of neurons resulting in an approximate solution. On the other hand, CHN gives a near-optimal solution. However, it takes too much time to simulate a differential equation which provides a main characteristic of CHN. A matching problem using a graph matching technique can be cast into an optimization problem. A new method for two-dimensional object recognition using a Hopfield neural network is proposed. A Hybrid Hopfield Network(HHN), which combines the merit of both the Continuous Hopfield Network and the Discrete Hopfield Network, is proposed and some of the advantages such as reliability and speed are shown in this paper. Stable states of neurons are analyzed and predicted based upon theory CHN after the convergence in DHN.