In this paper, a heuristic is proposed to find out the reliability of a directed network by using directed acyclic graph. This directed network has imperfect nodes as well as imperfect links. Directed acyclic graph based reliability computation involves three main steps: in the first step, built the reliability function of the given directed network which is the union of all min-paths from source to sink. In the second step, apply a heuristic approach to order the given communication links and nodes of the given directed network. Finally apply Shannon's decomposition method to compute the reliability of the given directed network.