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In cognitive radio network, efficient spectrum sharing is one of the important functions which can enhance the overall spectrum utilization of whole network. However, it is still an unexplored issue to make unlicensed users choose the most suitable spectrum according to user demand and the spectrum characteristics. In this paper, a new demand-matching spectrum sharing (DMSS) algorithm based on game theory for non-cooperative cognitive radio network is proposed. Firstly, the model of the matching factors between the user demand and the spectrum characteristics is built up. Then by adopting demand-matching factor, the DMSS game is proposed and Nash equilibrium is solved by Nelder-Mead direct search method. DMSS enables each unlicensed user to access multiple appropriate channels by maximizing its own payoff. Numeral results reveal that DMSS achieves high performance in spectrum utilization percentage and spectrum efficiency of cognitive radio network when it reaches Nash equilibrium.