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A key challenge in cognitive radios (CR) network is how to adaptively and efficiently allocate transmission powers and spectrum among CR users according to the surrounding environment. In this paper, we propose a novel spectrum sharing based on our improved Quantum Genetic Algorithm (QGA) in a non-cooperative game for CR network. We improved the original QGA by quantum crossover operator, in order to overcome the shortcoming of the original QGA easily falling into a local extremum when used to optimize the continuous functions with many extrema. We used our improved QGA as a competitive strategy and conducted several simulations in two-user system and multi-user system. From simulation results, it is evident that the proposed improved QGA based spectrum sharing scheme has better convergence rate and higher sum capacity than GA based scheme even in multi-user CR system, namely up to 2bit/s/Hz increase in capacity. The simulation results also show that the population size of QGA affect sum capacity of cognitive radio system. The results demonstrated the effectiveness and the applicability of QGA in spectrum sharing in multi-user cognitive radio system.