Abstract: The connected dominating tree with bounded transmission delay problem (CDTT) is defined based on (α,β)-tree for the construction of connected dominating set (CDS) in wireless sensor network., distributed connected dominating tree (CDT) algorithm is proposed to construct a CDT-tree with limited total power while moderating the constraint of the transmission delays. Our distributed algorithm for CDS consists of two phases: firstly construct a maximal independent set (MIS) based on a unit disk graph,and then implement the CDT algorithm based on a double weighted, undirected graph satisfying the requirements of energy consumption, transmission delays simultaneously with O(n2) time, message complexity. The theoretical analysis, simulation results show that the CDT algorithm gives an effective solution to the CDTT problem, construct the CDS with combined constraints.