Grid Computing enables the flexible sharing with resources among various dynamically created virtual organizations. Task Scheduling in Grid environment is a very important problem. To utilize the Grid resources efficiently, an efficient task scheduling algorithm is helping to schedule the tasks to the resources with reduced makespan. The problem of mapping metatask to the machines is shown to be NP-Complete. The NP-Complete problem can be solved using heuristic approaches. The proposed heuristic approach is based on QoS requirements. This paper proposes a Guaranteed Best Effort QoS Algorithm (GBEQoS) which achieves user satisfaction with minimum time and cost constraint in completing the task execution. The experimental results reveal that the proposed GBEQoS algorithm achieves reduced makespan with higher user satisfaction.