We present a self-mixing terahertz-frequency gas spectroscopy technique using a multimode quantum cascade laser. A precision-micro-machined external waveguide module and a double-metal quantum cascade laser device are used increase the optical feedback and the laser's frequency tuning range. Methanol spectra are measured using two laser modes at 3.362 THz and 3.428 THz simultaneously, with more than 8 absorption peaks resolved over a 17-GHz bandwidth, which provide minimum detectable absorption coefficients of 2.7×10 -4 cm −1 and 4.9×10 −4 cm −1 , respectively. In contrast to all previous self-mixing spectroscopy, our multimode technique expands the sensing bandwidth significantly. This broadband spectroscopy technique can potentially be used for the identification and analysis of chemical, biological radiological and nuclear (CBRN) agents and explosives.