We present a continuous-filtering Vernier spectrometer operating in the 3.15–3.4 µm range, based on a femtosecond doubly resonant optical parametric oscillator, a cavity with a finesse of 340, a grating mounted on a galvo scanner, and two photodiodes. The spectrometer allows acquisition of one spectrum spanning 250 nm of bandwidth in 25 ms with 8 GHz resolution, sufficient to detect molecular lines at atmospheric pressure. An active lock ensures good frequency and intensity stability of the consecutive spectra and enables continuous signal acquisition and efficient averaging. The relative frequency scale is calibrated using a Fabry–Perot etalon or, alternatively, the galvo scanner position signal. We measure spectra of a calibrated CH4 gas sample as well as dry and laboratory air and extract CH4 and H2O concentrations by multiline fitting of model spectra. The figure of merit of the spectrometer is 1.7 × 10−9 cm−1 Hz−1/2 per spectral element and the minimum detectable concentration of CH4 is 360 ppt Hz−1/2, averaging down to 90 ppt after 16 s