Spectrum auction has been considered as an effective way for dynamic spectrum access. In this paper, we propose a novel spectrum auction framework which enables spectrum spatial reuse among secondary users (SUs) and the payment rule is optimized here. There are two stages during the framework: auction and payment. Auction phase, the winner determination problem (WDP) is modeled as a 0/1 knapsack problem, and the Genetic Algorithm is selected to solve it. Payment phase, a payoff function similar to the Second-Price Auction is made, to ensure that all the SUs can get non-negative utilities only with their truthful information. Finally, simulation experiments show that the proposed auction mechanism has a better performance in solving the problem of WDP.