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Task scheduling is critical in heterogeneous systems especially with the huge number of tasks transmitted over grid causing system delay. Since heuristics are proposing methods for solving heterogeneous computing systems, several techniques were proposed for the scheduling on grid computing systems to get better execution time. In this paper, a proposed new heuristic algorithm named Two Stages Tasks Transfer (TSTT) algorithm to enhance Tenacious Penalty Based scheduling (TPB) algorithm. Heterogeneous Computing Scheduling Problem (HCSP) mathematical model has been used, where the independent tasks assigned to heterogeneous machines with different characteristics. Twelve datasets with different heterogeneity level examined using different heuristic algorithms to compare the performance with our proposed algorithm. The proposed algorithm showed its efficiency in term of makespan, resource utilization metrics for set of tasks.