The resources management in a grid computing is a complicated problem. Scheduling algorithms play important role in the parallel distributed computing systems for scheduling jobs, and dispatching them to appropriate resources. An efficient task scheduling algorithm is needed to reduce the total Time and Cost for job execution and improve the Load balancing between resources in the grid. In grid computing, load balancing is a technique to distribute workload fairly across computational resources, in order to obtain optimal resource utilization with minimum response time, and avoid overload. Load balancing is a crucial problem to grid computing. In this paper, we address scheduling problem of independent tasks in the market-based grid. In market grids, resource providers can request payment from users based on the amount of computational resource that used by them. Beside we consider Makespan and Load balancing. In this paper, NSGA II with Fuzzy Adaptive Mutation Operator is used to address independent task assignments problems in parallel distributed computing systems. Results obtained proved that our innovative algorithm converges to Pareto-optimal solutions faster and with more quality.