In this paper we are proposing a new approach for tasks allocation in a massively parallel system using Finite Automata. On the basis of task flow model of finite automata., we find the turnaround time for a parallel system using finite automata as a directed acyclic graph in the second section of the paper we discuss regarding the finite automata and directed acyclic graph after that we change finite automata into DAG for massively parallel system. All the simulations are performing in Intel C++ parallel compiler and compare these results with several interesting scheduling algorithms and we get better turnaround time.