We realized the growth of terahertz quantum-cascade laser （THz QCL） by gas source molecular beam epitaxy （GSMBE）. Electrochemical capacitance-voltage method， Hall measurement and high-resolution x-ray diffraction were used to evaluate the crystalline quality of the THz QCL active region. Meanwhile， we used an ensemble Monte Carlo method to investigate the carrier transport characteristics in a resonant-phonon THz QCL. Level alignment and electron motion under different applied biases are discussed in detail.