Finding an optimal solution to the problem of scheduling an application modeled by a Directed Acyclic Graph (DAG) onto a distributed system is known to be NP-complete. The complexity of the problem increases when task scheduling is to be done in a heterogeneous computing system, where the processors in the network may not be identical and take different amounts of time to execute the same task. This paper introduces a Performance Effective Task Scheduling (PETS) Algorithm for Network of Heterogeneous system, with complexity O (v+e) (p+ log v), which provides optimal results for applications represented by DAGs. The performance of the algorithm is illustrated by comparing the schedule length, speedup, efficiency and the scheduling time with existing algorithms such as, Heterogeneous Earliest Finish Time (HEFT) and Critical-Path On a processor (CPOP) and Levelized Min Time (LMT) reported in this paper. The comparison study based on both randomly generated graphs and graphs of some real applications shows that PETS algorithm substantially outperforms existing algorithms.