This document describes a proposed grouping based job scheduling algorithm for grid computing that aims to maximize resource utilization and minimize job processing times. It discusses related work on job scheduling algorithms and then presents the steps of the proposed algorithm. The algorithm uses shortest job first, first-in first-out, and round robin scheduling to process jobs in groups. The algorithm is evaluated experimentally in MATLAB and shown to reduce total job processing time compared to using only first-in first-out scheduling. Graphs demonstrate the processing time improvements achieved by the combined scheduling approach.