Based on decomposition-coordination methodology in large scale systems theory and Lagrangian relaxation technique in mathematical programming, this paper deals with optimization method for scheduling dependent tasks with due dates on identical parallel machines. A novel two-level multiplayer hierarchical scheduling algorithm is proposed. By making the most of structural properties of the precedence graph of partial ordering task set, and introducing the concept of “feasible start time interval”, the proposed algorithm can be used for solving the scheduling problem under study effectively. Also it may De extended to the cases with uniform machines or unrelated machines.