Enumerating convex connected subgraphs from data flow graphs of application hot-spots is required when designing instructions for a configurable processor. To achieve fast enumeration, properties of convex subgraphs of directed acyclic graph are studied. Based on the properties of convex subgraphs and adjacency of vertices, AS (adjacent search), a novel algorithm for enumerating convex connected subgraphs satisfying I/O constraints is presented. Results of experiments show that AS algorithm is more efficient than the existing algorithm, and rate is 10～1000X as fast. While the existing algorithm fails on large scale data-flow graphs, the AS algorithm is still able to accomplish enumeration successfully.