To address the unreliability and inefficiency of the existing algorithms for Bluetooth scatternet formation, this paper proposes a new efficient algorithm, Bluetooth Growing Network (BGN) algorithm, which constructs Bluetooth scatternet by adding reserve links among its branch nodes so that the resulting scatternet can maintain a high degree of connectivity while avoiding exccessive redundant links. Extensive simulation results demonstrate that the scatternet constructed by BGN algorithm is efficient in terms of the number of bridge nodes, average data transmission distance, network reliablity and overall network traffic.