This paper addresses the problem of scheduling parallel communication-aware tasks onto networks of workstations in heterogeneous computing environments. Many previous works have focused on the scheduling problem from the aspect of computation. However, as the computational power of new-added workstations increases, the communication mechanism may become the bottleneck of the system. Therefore, an algorithm is proposed to schedule parallel tasks by considering the communication requirements of the applications and the network bandwidth. Experimental results show the superiority of the algorithm over that presented in previous literature.