This paper presents a three-stage greedy and neural-network algorithm for the subgraph isomorphism problem. Given two graphs of G=(V/sub 1/,E/sub 1/) and H=(V/sub 2/,E/sub 2/), the goal of this NP-complete problem is to find a subgraph of H isomorphic to G. The proposed algorithm consists of three stages. The first stage extracts a set of vertices in H which may be assigned to each vertex in G, based on the newly defined necessary condition. The second stage sequentially seeks a solution based on a greedy method by assigning each vertex in G to a vertex in H satisfying the constraints in descending order of degrees. After the second stage fails at all, the third stage resolves the constraints in parallel based on a digital neural network, where the best result in the second stage is partially adopted to reduce the search space. The performance is evaluated by solving randomly generated graph instances, where the simulation results show that our algorithm achieves the high solution quality in reasonable computation time.