Auction was widely used to tackle spectrum allocation and sharing in the secondary market under the condition of spectrum scarcity.In real communication system,such as broadband communication,the utilization of spectrum resource is various because of different requirements and complex application scenarios.So,these schemes cannot be directly applied to the above wireless communication system.To solve this problem,a new model where sellers/buyers can sell/buy multi-unit for heterogeneous spectrum was proposed and a truthful multi-unit double auction framework was designed for heterogeneous spectrum trading.A valuation function is first applied to represent the buyer\'s true valuation of the sub-band and reflect the buyer\'s satisfaction degree and a novel concept termed\'virtual player\'was introduced.Then the buyer group was constructed based on the conflict graph to reuse the same spectrum among interference-free buyers in both spatial and temporal domains.The winner determination strategy and algorithm of clearing price were designed elaborately.According to the theoretical analysis,the scheme can satisfy three critical economic properties:truthfulness,individual rationality,and budget balance.Finally,simulation results show that the proposed scheme can achieve better user satisfaction,auction efficiency and spectrum reuse rate for the real communication system.The proposed auction framework is practical and effective.