Direct deposition of graphene layers on the flexible glass fiber surface to form the three-dimensional (3D) core-shell structures is offered using a two-heating reactor chemical vapor deposition system. The two-heating reactor is utilized to offer sufficient, well-proportioned floating C atoms and provide a facile way for low-temperature deposition. Graphene layers, which are controlled by changing the growth time, can be grown on the surface of wire-type glass fiber with the diameter from 30 nm to 120 um. The core-shell graphene/glass fiber deposition mechanism is proposed, suggesting that the 3D graphene films can be deposited on any proper wire-type substrates. These results open a facile way for direct and high-efficiency deposition of the transfer-free graphene layers on the low-temperature dielectric wire-type substrates.PACS81.05.U-; 81.07.-b; 81.15.Gh