We demonstrate an experimental scheme to simultaneously stabilize the frequency and amplitude of a 3.5 THz third-order distributed feedback quantum cascade laser as a local oscillator. The frequency stabilization has been realized using a methanol absorption line, a power detector, and a proportional-integral-derivative (PID) loop. The amplitude stabilization of the incident power has been achieved using a swing-arm voice coil actuator as a fast optical attenuator, using the direct detection output of a superconducting mixer in combination with a 2nd PID loop. Improved Allan variance times of the entire receiver, as well as the heterodyne molecular spectra, are demonstrated. A terahertz (THz) quantum cascade laser (QCL) is the most promising solid-state source as the local oscillator (LO) for a high resolution heterodyne receiver operating at frequencies above 2 THz and, in particular, for a multi-pixel array receiver because of its high output power (typically mW). 1,2 Among different types of applications, a super-THz heterodyne receiver plays a vital role in astronomical observations, for instance to map a large number of fine structures and molecular lines associated with the formation of stars and planets in the Milky Way and nearby galaxies. 3 Those spectral lines at high frequencies are typically narrow ( a few MHz). Furthermore, the signals are, in general, very weak and deeply embedded within the noise. 3 The narrow spectral lines require either frequency or phase stabilization of a local oscillator. Since the intrinsic linewidth of a THz QCL is much narrower (