A Grid is a decentralized, high performance computing environment. Grids are often large scale, geographically distributed heterogeneous system, in which resources belong to individual or multiple organizations. Resource allocation and job scheduling are the two difficult tasks in grid computing. The key challenge in grid computing is the efficient job scheduling and resource management. Large-scale scientific applications require numerous resources for execution. Effective utilization of computational grid resources requires efficient scheduling of jobs to the available grid resources. To adapt to the heterogeneity and dynamism of the grid environment an efficient job scheduling algorithm is required to minimize the makespan with maximum resource utilization. This paper proposes a new enhanced heuristic Min-mean scheduling algorithm.