The broadband terahertz wave, with its correspondence to the fingerprint spectra of gas molecules and relatively high transmittance through smoke, aerosol, and combustion environments, bears great potential for gas detection and combustion diagnostics. While access to the rotational spectral fingerprints in the terahertz region provides opportunities for species-selective diagnostics with minimized background and cross interference, few studies have been devoted to direct, quantitative, simultaneous analysis of multiple components exploiting the terahertz region. In this work, we achieve quantitative measurements of CO, NH3 and H2O gas concentrations at standard temperature and pressure over a bandwidth of 1 THz, using direct absorption spectrum from femtosecond-laser-based terahertz time-domain spectroscopy. Spectral fitting of the fully resolved rotational lines yields good precision and accuracy with validation against calibrated mixtures. The estimated detection limts of the multi-speices sensing system are 250 ppm·m, 7 ppm·m and 4 ppm·m for CO, NH3 and H2O, respectively. The demonstration of quantitative, multi-species gas sensing indicates the feasibility and practical value of using broadband terahertz absorption spectroscopy for real-time, quantitative analysis and speciation of multicomponent gas in complicated practical environments such as combustion and multi-phase flows.