Due to spectrum scarcity and its inefficient usage, many emerging services going wireless are in shortage of spectrum resources. Auction has been widely used for resource allocation in many fields. Spectrum auction is deemed as a promising solution to relieve the conflict between scarce spectrum resource supply and ever-increasing demand, which could achieve the optimal of the spectrum reallocation through the market competition. Existing researches on spectrum auction mainly focus on spectrum spatial reuse and spectrum utilization. Nevertheless, their clearing price often deviates from actual value of spectrum because of too small market scale, and the blindness of buyers' bid factors are not taken into consideration. To solve the above problem, a completely-competitive-equilibrium-based double spectrum auction mechanism (ComDSA) is proposed. Firstly, multi-player game between players can be modeled as double-person game between person and nature. And then, the probability of market types and Harsanyi transformation are introduced in ComDSA to transform the problem into complete information game. Finally, the clearing price achieves the completely competitive equilibrium through multi-round bidding according to continuous bidding model. Solid theoretical analysis and extensive simulation study illustrate the improvement of spectrum reuse and transaction rate on the basis of completely competitive equilibrium.