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The increasing demand for grid computing resources calls for an incentive-compatible pricing mechanism for differentiated service qualities. Costeffective scheduling of grid workflow applications described by Directed Acyclic Graph (DAG) becomes an essential and complex problem. In general, the optimization problem is NP-hard, and heuristics are among the methods of choice. In this paper, in order to taking advantage of the workflow deadline, several priority rules are developed, which take into account both activity information and service levels information. To invalidate their effectiveness, these priority rules are applied to different initial solutions. Computational experiments show that two heuristics combining priority rules GRBPA, GRPA with starting solution HL can achieve the better results than heuristics based on other priority rules.