In this paper, we propose a heuristic algorithm based on dynamic critical path (DCP) to solve the problem of task scheduling on networks of workstations (NOW). The algorithm takes into account both the characteristics of DCP and NOW by intelligently pre-allocating network communication resources so as to avoid potential communication conflict. It has a reasonable computational complexity of O(v^2(1+p)), where v is the number of nodes in the task graph and p is the number of processors in the NOW. It is suitable for regular as well as irregular task graphs. The algorithm when tested under various task graphs shows performance much superior to previously known techniques.