Abstract: In this paper, a market-based approach is presented to allocate grid resources, which is based on equilibrium theory and which realizes the optimal allocation of grid resources by the market mechanism. Firstly, the agent-based framework of resources allocation is described, which can be divided into three levels: Resources level, agents level and users level. Secondly, a market model of resources allocation in computer grids is given, in which the utility function is used to characterize the content degree of a user for some given resources. Thirdly, the equilibrium state in a market model is defined and a proof of its optimality is given, which means resources allocation is not only efficient but also fair in the equilibrium. Finally, an iterative algorithm of resource-agents is introduced.