Abstract: Spectrum sharing problem in multi-channel cognitive radio networks was modeled as a cooperative game. A utility function based on the product of the signal to interference plus noise ratio （SINR） was proposed. The power allocation of secondary users was determined by maximizing the product of the utility function to ensure that the interference power to the primary user is under a certain threshold in each channel. As the problem of maximization the product of the utility function of secondary users was non-convex, it was transformed into an equivalent convex optimization problem by variable alternation. A spectrum sharing algorithm was proposed based on the dual decomposition of the convex optimization problem. Simulation results show that the proposed algorithm achieves an effective compromise between the sum rate and the fairness among the secondary users.