Abstract: This study present a QoS based predictive Max-Min, Min-Min Switcher (QPSMax-Min<>Min-Min) algorithm for scheduling jobs in a grid. The algorithm makes an appropriate selection among the QoS based Max-Min or QoS based Min-Min algorithm on the basis of heuristic applied, before scheduling the next job. The effect on the execution time of grid jobs due to non-dedicated property of resources has also been considered. The algorithm uses the history information about the execution of jobs to predict the performance of non-dedicated resources. Simulation demonstrates that (QPSMax-Min<>Min-Min) outweighs the traditional QoS guided algorithms a lot in makespan.