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Desirable goals for grid task scheduling algorithms would shorten average delay, maximize system utilization and fulfill user constraints. In this work, an agent-based grid management infrastructure coupled with mean field annealing (MFA) scheduling algorithm has been proposed. An agent in grid utilizes a neural network algorithm to manage and schedule tasks. The Hopfield neural network is good at finding optimal solution with multi-constraints and can be fast to converge to the result. However, it is often trapped in a local minimum. Stochastic simulated annealing algorithm has an advantage in finding the optimal solution and escaping from the local minimum. Both significant characteristics of Hopfield neural network structure and stochastic simulated annealing algorithm are combined together to yield a mean field annealing scheme. A modified cooling procedure to accelerate reaching equilibrium for normalized mean field annealing has been applied to this scheme. The simulation results show that the scheduling algorithm of MFA works effectively.