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Cognitive Radio (CR) is a promising technology for dynamic spectrum access with the ability of observing the surrounding environment and adapting itself to the change of network environment. For the problem of spectrum sharing among a primary user and multiple secondary users based on Game Theory, an improved utility function of the second user is proposed. In this function, the influence of the shared spectrum on the spectrum demand is considered. The more spectrum the second user shared, the demand for spectrum is relatively less. The demand degree in the utility function is a function of spectrum sharing, so it is a variable which can more accurately describes the cognitive radio system features. The theoretical analysis and simulation results show the validity of the proposed algorithm and the existence of Nash equilibrium. With the improved utility function, the fairness is introduced to the process of spectrum sharing.