Concise open-path continuous-wave cavity ring-down spectroscopy (CW-CRDS) with a bow-tie cavity structure is demonstrated in the single- and dual-optical-path experiments for multicomponent gas detection, e.g., greenhouse gas concentration evaluation in ambient air. Owing to its features of optical feedback suppression and small free spectral range (FSR), the bow-tie configuration shows its special advantages in the realization of both a compact arrangement and two counter-propagating non-interference optical paths. The minimum of the Allan deviation reaches 1.6×10-10 cm-1 for an integration time of 100 s, corresponding to the noise equivalent absorption coefficient of 1.6×10-9 cm-1 Hz-1/2. The detection sensitivity of methane is deduced to be 0.9 ppbv with its absorption cross section of 1.48×10-20 cm2/molecule in the 512 decays averaging mode. A wavelength-correction method is proposed to reduce by about 30% the uncertainty in the measurements caused by the deviation in the wavelength resonance between incident laser and ring-down cavity. The concentrations of greenhouse gases in ambient air are measured by the open-path CW-CRDS with the uncertainties of 0.02, 100, and 10 ppmv for CH4, H2O, and CO2, respectively.