By day to day developing the grid systems, it is necessary to apply new methods for allocating the resources to achieving the high performance in heterogeneous computing environment. This paper aims to seeking for a new approach by which one can allocate the tasks using a modified version of Ant Colony Optimization algorithm such that this algorithm cannot be involved in local minimum. Tasks will be entered to the system by Directed Acyclic Graph (DAG). This method tried to allocate the tasks to the processors in short time