A surface-emitting THz parametric oscillator is set up to generate a narrow-linewidth, nanosecond pulsed THz-wave radiation. The THz-wave radiation is coherently detected using the frequency up-conversion in MgO: LiNbO(3) crystal. Fast frequency tuning and automatic achromatic THz-wave detection are achieved through a special optical design, including a variable-angle mirror and 1:1 telescope devices in the pump and THz-wave beams. We demonstrate a frequency-agile THz-wave parametric generation and THz-wave coherent detection system. This system can be used as a frequency-domain THz-wave spectrometer operated at room-temperature, and there are a high possible to develop into a real-time two-dimensional THz spectral imaging system.