Terahertz time-domain spectroscopy (THz-TDS) has emerged as a powerful tool for materials characterization and imaging. A trend towards size reduction, higher component integration and performance improvement for advanced THz-TDS systems is of increasing interest. The use of single semiconducting nanowires for terahertz (THz) detection is a nascent field that has great potential to realize future highly-integrated THz systems. In order to develop such components, optimized material optoelectronic properties and careful device design are necessary. Here, we present antenna-optimized photoconductive detectors based on single InP nanowires with superior properties of high carrier mobility (∽1260 cm2V-1s-1) and low dark current (∼10 pA), which exhibit excellent sensitivity and broadband performance. We demonstrate that these nanowire THz detectors can provide high quality time-domain spectra for materials characterization in a THz-TDS system, a critical step towards future application in advanced THz-TDS system with high spectral and spatial resolution.