The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. The primary goal of topology control is to design power-efficient algorithms that maintain network connectivity and optimize performance metrics such as nodes lifetime and throughput. An energy-efficient distributed topology-control algorithm is proposed, briefly called VCGG (A varying-cone distributed topology-control algorithm on Gabriel graph). Using a new mechanism of selecting the logic neighbor nodes by firstly deleting the farthest node (FDFN), the VCGG algorithm builds a degree-bounded, power spanner and planar subgraph by making use of merit of the varying cone. The simulation results show that the VCGG algorithm performs better, in terms of power efficiency, number of communication neighbors and interference, than the existing SΘGG and SYaoGG algorithms.