Grid computing, one of the most trendy phrase used in IT, is emerging vastly distributed computational paradigm. A computational grid provides a collaborative environment of the hefty number of resources capable to do high computing performance to reach the common goal. Grid computing can be called as super virtual computer, it ensemble large scale geographically distributed heterogeneous resources. Resource allocation is a key element in the grid computing and grid resource may leave at anytime from grid environment. Despite a number of benefits in grid computing, still resource allocation is a challenging task in the grid. This work investigates to maximize the profits by analyzing how the tasks are allocated to grid resources effectively according to quality of service parameter and gratifying user requisition. A fusion of SS-GA algorithm has introduced to answer the above raised question about the resource allocation problem based on grid user requisition. The swift uses genetic algorithms heuristic functions and makes an effective resource allocation process in grid environment. The result of proposed fusion of SS-GA algorithm ameliorates the grid resource allocation.