One-dimensional semiconductors are promising materials for high-performance nanoscale devices. Using the first-principles calculations combined with deformation potential approximation, we study the electronic structures and carrier transport properties of black phosphorus nanotubes (BPNTs). It is found that both armchair and zigzag BPNTs with diameter 13.5-18.5 angstrom are direct bandgap semiconductors. At a similar diameter, the carrier mobility of zigzag BPNT is one order of magnitude larger than that of armchair BPNT. For armchair BPNTs, the electron mobility is about 90.70-155.33 cm(2) V-1 s(-1) at room temperature, which is about three times of its hole counterpart. For zigzag BPNTs, the maximum mobility can reach 2.87 x 10(3) cm(2) V-1 s(-1). Furthermore, the electronic properties can be effectively tuned by the strain. For zigzag (0,13) nanotube, there is a direct-to-indirect band gap transition at a tensile strain of about 6%. Moreover, the electron mobility is boosted sharply by one order of magnitude by applying the compressive or tensile strain. The electron mobility increases to 14.05 x 10(3) cm(2) V-1 s(-1) at a tensile strain of 9%. Our calculations highlight the tunable electronic properties and superior carrier mobility of BPNTs that are promising for interesting applications in future nano-electronic devices. (C) 2018 Elsevier B.V. All rights reserved.