The active region of GaAs/AlGaAs bound-to-continuum terahertz quantum-cascade laser （THz QCL） is grown by gas-source molecular beam epitaxy. The device fabrication process of semi-insulating surface-plasmon THz QCL is studied in detail. The electrical and optical characteristics of the fabricated THz QCL device are measured using a far-infrared Fourier transform infrared spectrometer with a deuterated triglycerine sulfate far-infrared detector. At 10 K，the measured lasing frequency is 32 THz and the threshold current density is 275 A/cm2.