Abstract: Grid Computing Systems, with their focus on Creative applications, high-performance orientation and large-scale resource sharing, have emerged as a significant new field. One of the important goals in any computational grid environment is to achieve effectual allocation with fault tolerance to complete the task on time. Optimal resource allocation and the fault tolerance system’s failure rate remain a problem in the current system. To address the above-mentioned issues, The Fit First(FF) heuristic algorithm and the Adaptive particle Swarm Optimization (APSO) algorithm are proposed in this research to improve grid system efficiency and resource allocation. The proposed system involves resource allocation using the APSO algorithm, path and node-level fault tolerance and multiple resource formation using the FF heuristic algorithm for better efficiency. Consider the number of tasks, number of resources and number of grid users at first when considering grid computing. The APSO algorithm is used to select more optimal resource efficiently in this work, and it is used to control resource allocation. The optimal tools for the user requirements are chosen by generating objective functions using the best fitness value. It is used to provide Quality of Service (QoS) in terms of lower costs, quick response and satisfaction with the best services. The fault tolerance is implemented using the FF heuristic algorithm, which increases the data transfer time and reduces failure time. The grid efficiency can be improved by reducing resource idle time and evenly spreading unmapped tasks among the available resources. The simulation results show that the proposed APSO+FF algorithm outperforms the current algorithm in time complexity, error rate, cost complexity, and accuracy. Keywords: Grid computing, Adaptive Particle Swarm Optimization (APSO) algorithm, Fit First (FF) heuristic algorithm, fault tolerance, resource allocation.