A neural network approach to finding trajectories of feature points in a monocular image sequence is proposed. In conventional methods, this problem is formulated as an optimization problem and solved using heuristic algorithms. The problem usually involves lengthy computations, making it computationally difficult. We apply the Hopfield neural network to image sequence correspondence. The design and development of the Lyapunov function for this problem are discussed in detail. Furthermore, the neural-network-based image correspondence scheme is extended to the case of successive image frames, in which some feature points are allowed to be occluded. Examples and simulation results are presented to illustrate the design process and the convergence characteristics of the proposed neural network. By using the massive parallel-processing power of neural networks, a real-time and accurate solution can be obtained.