Graphs are widely used to model complicated data semantics in many applications. In this paper we propose Fast-ON, an efficient algorithm for subgraph isomorphism problem which has proven to be NP-complete. Fast-ON is based on Ullman algorithm [1]. It improves the search space of Ullman algorithm by considering two effective optimizations. Comparing to the well-known algorithms Ullman and Vflib [2], Fast-ON achieves up to 1–3 orders of magnitude speed-up.