The one-dimensional (1D) acceptor-donor (A-D) hetero-nanotube (HNT) has attracted much attention as a potential candidate for a channel structure of next-generation field effect transistors (FETs). Herein, we designed A-D CN/CB double-wall (dw) HNTs by coaxially wrapping CN and CB nanotubes together. By using density functional theory (DFT) combined with the nonequilibrium Green's function (NEGF) formalism, we studied the electronic properties and ballistic transport behavior of CN/CB dwHNTs in comparison with the ones in vertical stacking contact. The remarkable charge transfer between CN and CB nanotubes and band hybridization in CN/CB dwHNTs originate from the strong intertubular π-π stacking interaction. In the simulated all-around-gated FET devices, (12,0) CN/(6,0) CB dwHNT with 2 repeated wrapping units possesses the optimal performance, including rectifying ratio and subthreshold swing (SS), by enhancing the A-D asymmetry. Our work suggests that coaxial wrapping is a method superior to vertical stacking in constructing A-D HNTs for high-performance electronic and optoelectronic devices based on 1D materials.