Grid is an infrastructure that involves the integrated and collaborative use of computer, networks, databases and scientific instruments owned and managed by multiple organizations. The Grid computing aggregates the power of widely distributed heterogeneous resources and provides non-trival services to the users to resolve large scale data intensive problems in various fields like science, engineering and commerce. Load balancing and Resource management are the two major challenging tasks in the Grid Computing infrastructure. These two tasks are interdependent, Load balancing is a mechanism which equally spreads the load among available resources and Resource management is to select the appropriate resource for a particular task in such a way that overall efficiency can be achieved. Many algorithms have been designed for scheduling of task in Grid environment some of the popular heuristic algorithms are Opportunistic Load Balancing (OLB), Min-Min, Fast Greedy, Tabu-Search, Max-Min, Minimum Execution Time (MET) and Minimum Completion Time (MCT) etc. All these algorithms are based on different characteristics of ant and work to minimize the total execution time of tasks and total cost of a using a resource. The objective of the dissertation is to propose a heuristic resource scheduling algorithm (HRSA) based on ant algorithm that can perform resource allocation efficiently and effectively in terms of minimizing the total execution time and cost. The simulation results show that the proposed algorithm is capable of reducing the total execution time of the task and cost of the resource in comparison of random resource scheduling algorithm (RRSA) implemented with TIME_SHARED (Round-Robin) or SPACE_SHARED (FCFS) resource allocation policy. A JAVA based event simulation toolkit called GridSim4.0 is used for performance evaluation of the algorithm. The toolkit provides facilities for modeling and simulating grid resources, tasks and network connectivity with different capabilities and configurations.