The need of processing graph reachability queries stems from many applications that manage complex data as graphs. The applications include transportation network, Internet traffic analyzing, Web navigation, semantic web, chemical informatics and bio-informatics systems, and computer vision. A graph reachability query, as one of the primary tasks, is to find whether two given data objects, u and v, are related in any ways in a large and complex dataset. Formally, the query is about to find if v is reachable from u in a directed graph which is large in size. In this paper, we focus ourselves on building a reachability labeling for a large directed graph, in order to process reachability queries efficiently. Such a labeling needs to be minimized in size for the efficiency of answering the queries, and needs to be computed fast for the efficiency of constructing such a labeling. As such a labeling, 2-hop cover was proposed for arbitrary graphs with theoretical bounds on both the construction cost and the size of the resulting labeling. However, in practice, as reported, the construction cost of 2-hop cover is very high even with super power machines. In this paper, we propose a novel geometry-based algorithm which computes high-quality 2-hop cover fast. Our experimental results verify the effectiveness of our techniques over large real and synthetic graph datasets.