In this chapter, we propose a novel resource-scheduling strategy capable of handling multiple resource requirements for jobs that arrive in a Grid Computing Environment. In our proposed algorithm, referred to as Multi-Resource Scheduling (MRS) algorithm, we take into account both the site capabilities and the resource requirements of jobs. The main objective of the algorithm is to obtain a minimal execution schedule through efficient management of available Grid resources. We introduce the concept of a 2-dimensional virtual map and resource potential using a co-ordinate based system. To further develop this concept, a third dimension was added to include resource availabilities in the Grid environment. Based on the proposed model, rigorous simulation experiments shows that the strategy provides excellent allocation schedules as well as superior avoidance of job failures by at least 55%. The aggregated considerations is shown to render high-performance in the Grid Computing Environment. The strategy is also capable of scaling to address additional requirements and considerations without sacrificing performance. Our experimental results clearly show that MRS outperforms other strategies and we highlight the impact and importance of our strategy.