Summary: Most scheduling heuristics applied to Heterogeneous Computing (HC) focus on the search of a minimum makespan, instead of the reduction of cost. However, relevant studies presume that HC is based on high-speed bandwidth and communication time has ignored. Furthermore, in response to the appeal for a user-pay policy, when a user submits a job to a Grid environment for computation each implementation of a job would be charged. Therefore, the Apparent Tardiness Cost Setups-Minimum Completion Time (ATCS-MCT) scheduling heuristic considers both makespan and cost, and it composes of execution time, communication time, weight and deadline factors. This study simulates experiments in a dynamic environment, due to the nature of Grid computing being dynamic. The ATCS-MCT is compared to frequent solutions by five scheduling heuristics. This study indicates that the ATCS-MCT achieves a similarly smaller makespan, and lower cost than Minimum Completion Time (MCT) scheduling heuristic, which is the benchmark of on-line mapping.