Grid computing, one of the most contemporary phrase used in IT, is appearing enormously distributed computational paradigm. Despite a number of profits in grid computing, still resource allotment is a challenging task in the grid. This work defines to increase the benefits by analyzing how the tasks are allocated to grid resources effectively according to quality of service parameter and gratifying user requisition. A method of conservative backfilling load balancing with random search algorithm has introduced to answer the above raised question about the resource allocation problem based on grid user requisition. The result of proposed method of CNBF-RS algorithm ameliorates the grid resource allocation.