The grid computing is one of the strong initiatives and technologies that has been introduced in the last decade for improve the resources utilization, optimization and provide very high throughput computation for wide range of applications. To attain these goals an effective scheduling for grid systems is a vital issue to realize the intended performance. The processes scheduling could be executed in various methods and protocols that have been extensively address in the literature. This works utilized shortest process first (SPF) protocol which gives the shortest jobs the highest priorities. For longer jobs, it should have lower priorities and wait in the queue longer time. With too many smallest tasks reach the queue, the long tasks can't have an opportunity to be processed and the number of tasks continue growing in front of them, which is well-known issue called Starvations. In this work we introduce a new time quantum-based for shortest process first to avoid the starvation problem. The objective of the model is to optimize the utilization of resources by reducing end time of the job and enhancing performance of job scheduling. The model introduces fair treatment for all the processes. A simulation environment for the proposed model is developed and implemented. The results show that the quantum time-based solution has improved the starvation issues severely in terms of time delay, optimization of grid resources and fairness. The results show that SJF with time quantum outperform the SJF in terms of end time process, resources utilization, delay to transmission and Fair treatment for all the processes. But in term of waiting time Shortest Job First is better, SJF does not always minimize waiting time.