Attributed graph is widely used for modeling a variety of information networks, such as the web, sensor networks, biological networks, economic graphs, and social networks. Given the high popularity of attributed graph, in this paper, we study one of the most fundamental graph query types for attributed graph — the reachability query with attribute constraints i.e. ‘Is there a path from source to destination such that all attributes on the path satisfy given attribute constraints?’. We first introduce a new approach which takes the advantage of a ‘perfect’ hash function for compressing a multi-dimensional attribute into a unique hash value so as to bound the expected cost of secondary storage access (e.g. SDD I/O, remote data access). Then, we propose a synopsis based heuristic search technique to further reduce the CPU and secondary storage access cost. For both techniques, the index construction time and space are still linear to the topology size. An extensive experimental evaluation using real and synthetic graphs demonstrates the superiority of our proposed techniques.