ABSTRACT As an important anode material for fast-charging Li-ion batteries (LIBs), black phosphorus (BP) has attracted extensive attention. Black phosphorene nanotubes (BPNTs) can be theoretically produced by rolling up the black phosphorene nanosheet along armchair (a-BPNTs) and zigzag (z-BPNTs) directions. The effects of curvature, chirality, Li-storage concentrations and strain stress on the Li-storage performance such as Li diffusion barriers and mechanical stabilities of BPNTs are mainly investigated by first principles calculations. The theoretical calculations predict that the a-BPNTs and z-BPNTs have good maximum Li-storage capacities, and the z-BPNTs exhibit better flexibility than a-BPNTs. The mechanical stabilities and Li-migration are all related to the curvature of BPNTs. Additionally, both a-BPNTs and z-BPNTs exhibit fast Li-ion conductivity along the c-axis direction. Moreover, the average Poisson's ratio of a-BPNTs (0.68) is larger than that of z-BPNTs (0.17), indicating that the strain stress is more difficult to apply on a-BPNTs than z-BPNTs. Our calculations predict that the a-BPNTs can afford ultrafast kinetic rate for fast-charging and high-power LIBs, while the z-BPNTs can provide extra capacity for high-energy LIBs.