Terahertz (THz) Time domain spectroscopy (THz-TDS) is a broadband spectroscopic technique spreading its uses in multiple fields: in science from material science to biology, in industry where it measures the thickness of a paint layer during the painting operation. Using such practical commercial apparatus with broad spectrum for gas spectroscopy could be a major asset for air quality monitoring and tracking of atmospheric composition. However, gas spectroscopy needs high resolution and the usual approach in THz-TDS, where the recorded time trace is Fourier transform, suffers from resolution limitation due to the size of the delay line in the system. In this letter, we introduce the concept of constraint reconstruction for super-resolution spectroscopy based on the modeling of the spectroscopic lines in a sparse spectrum. Light molecule gas typically shows sparse and narrow lines on a broad spectrum and we propose an algorithm reconstructing these lines with a resolution improvement of 10 the ultimate resolution reachable by the apparatus. We envision the proposed technique to lead to broadband, selective, rapid and cheap gas monitoring applications.