Grid computing encourages utilization of idle, distributed resources existing worldwide to solve complex problems which are computational and data intensive. The problem is divided into independent sub problems called as jobs and they are executed by the resources available in the grid. Scheduling these jobs to different heterogeneous resources of a grid is an important issue and is considered as a NP complete problem. Hence, it is required to have a good job scheduling strategy to utilize the distributed grids effectively. In order to solve this issue, many heuristic approaches have been proposed in the literature that gives near optimal solution. The evolutionary Genetic Algorithm using Multiple QoS (Quality of Service) satisfaction for scheduling independent tasks on heterogeneous grid resources in offline mode is proposed.