A heterogeneous computing system (HCS) efficiently utilizes the heterogeneity of diverse computational resources interconnected with high speed networks to execute a group of compute intensive tasks. These are typically represented by means of a directed acyclic graph (DAG) with varied computational requirements and constraints. The optimal scheduling of the given set of precedence-constrained tasks to available resources is a core concern in HCS and is known to be NP-complete problem. Task prioritization has been a major criterion for achieving high performance in HCS. This paper presents a SD-Based Algorithm for Task Scheduling (SDBATS) which uses the standard deviation of the expected execution time of a given task on the available resources in the heterogeneous computing environment as a key attribute for assigning task priority. This new approach takes into account the task heterogeneity and achieves a significant reduction in the overall execution time of a given application. The performance of the proposed algorithm has been extensively studied under a variety of conditions on standard task graphs from Graph Partition Archive as well as on some real world application DAGs such as Gaussian Elimination and Fast Fourier Transformation application DAGs. Our results show that SDBATS outperforms well known existing DAG scheduling algorithms in terms of schedule length (make span) and speedup. © 2013 IEEE.