A cavity ring-down spectrometer is built for trace gas detection using telecom distributed feedback (DFB) diode lasers. The longitudinal modes of the ring-down cavity are used as frequency markers without active-locking either the laser or the high-finesse cavity. A control scheme is applied to scan the DFB laser frequency, matching the cavity modes one by one in sequence and resulting in a correct index at each recorded spectral data point, which allows us to calibrate the spectrum with a relative frequency precision of 0.06 MHz. Besides the frequency precision of the spectrometer, a sensitivity (noise-equivalent absorption) of 4×10-11 cm-1 Hz-1/2 has also been demonstrated. A minimum detectable absorption coefficient of 5×10-12 cm-1 has been obtained by averaging about 100 spectra recorded in 2 h. The quantitative accuracy is tested by measuring the CO2 concentrations in N2 samples prepared by the gravimetric method, and the relative deviation is less than 0.3%. The trace detection capability is demonstrated by detecting CO2 of ppbv-level concentrations in a high-purity nitrogen gas sample. Simple structure, high sensitivity, and good accuracy make the instrument very suitable for quantitative trace gas analysis.