Grid computing has emerged as an important field from the distributed and parallel computing where the resources of various computers in the network are used to solve a particular problem, because of high demand of computational power and need of high performance. To achieve the promising potential of grid computing, an effective and efficient job scheduling is required. Job scheduling is used to schedule the user jobs to appropriate resources in grid environment. Min-Min is the most simple and well known scheduling algorithm in grid computing that is used to minimize the makespan. The drawback of min-min algorithm is that the schedule produced by min-min is not optimal with respect of load balancing and it is not effective for resource utilization and one resource can execute one job at a time, the number of resources is known in prior. In this paper, a Min-Min Ant Colony (MMAC) algorithm is proposed that reduces the makespan and maximize the resource utilization using the features of both min-min algorithm and ant colony optimization. It is a two phase algorithm.