In this paper we study a social welfare maximization problem for spectrum sharing in cognitive radio networks. To fully use the spectrum resource, the spectrum owned by the licensed primary user (PU) can be leased to secondary users (SUs) for transmitting data. We first formulate the social welfare of a cognitive radio network, considering the cost for the primary user sharing spectrum and the utility gained for secondary users transmitting data. The social welfare maximization is a convex optimization, which can be solved by standard methods in a centralized manner. However, the utility function of each secondary user always contains the private information, which leads to the centralized methods disabled. To overcome this challenge, we propose an iterative distributed algorithm based on a pricing-based decomposition framework. It is theoretically proved that our proposed algorithm converges to the optimal solution. Numerical simulation results are presented to show that our proposed algorithm achieves optimal social welfare and fast convergence speed.