The material of GaAs/AlGaAs bound-to-continuum terahertz quantum-cascade laser (THz QCL) was grown by gas source molecular beam epitaxy. A THz QCL device was fabricated with semi-insulating surface-plasmon waveguide. Its spectrum and light intensity-current-voltage characteristics were studied. The device emits about 2.95 THz, and yields a maximum temperature of 67 K in pulse mode. In continuous-wave mode, it displays a threshold current density of 230 A/cm2 at 9 K with maximum emitted power of 1.2 mW and lases up to 30 K.