Developing single-nanowire terahertz (THz) electronics and employing them as sub-wavelength components for highly-integrated THz time-domain spectroscopy (THz-TDS) applications is a promising approach to achieve future low-cost, highly integrable and high-resolution THz tools, which are desirable in many areas spanning from security, industry, environmental monitoring and medical diagnostics to fundamental science. In this work, we present the design and growth of n+-i-n+ InP nanowires. The axial doping profile of the n+-i-n+ InP nanowires has been calibrated and characterized using combined optical and electrical approaches to achieve nanowire devices with low contact resistances, on which the highly-sensitive InP single-nanowire photoconductive THz detectors have been demonstrated. While the n+-i-n+ InP nanowire detector has a only pA-level response current, it has a 2.5 times improved signal-to-noise ratio compared with the undoped InP nanowire detector and is comparable to traditional bulk THz detectors. This performance indicates a promising path to nanowire-based THz electronics for future commercial applications.