Since there is no fixed infrastructure or centralized management in wireless sensor networks (WSNs), a connected dominating set (CDS) has been proposed as a virtual backbone. The CDS plays a major role in routing, broadcasting, coverage and activity scheduling. To reduce the traffic during communication and prolong network lifetime, it is desirable to construct a minimum CDS (MCDS). The MCDS problem has been studied intensively in unit disk graph (UDG), in which the nodes have the same transmission range. In real world this kind of networks are not necessarily contain nodes with equal transmission range. Recently one research has investigated the MCDS problem in disk graph with bidirectional links (DGB), in which nodes have different transmission ranges. This approach has constant approximation ratio with time and message complexity of O(n²). In this paper, a new distributed algorithm for MCDS problem in DGB with constant approximation ratio is introduced which has outstanding time and message complexity of O(n). Theoretical analysis and simulation results are also presented to verify our approach's efficiency.