We put forward a double-looped Mach-Zehnder interferometer for acquiring continuous ring-down interferograms with two fiber-loop cavities with slightly different optical path lengths. Each group of pulses through the sample and reference loops creates a ring-down pulse train with equal time intervals in Vernier fashion, and interferes with each other to produce multiple ring-down interferograms successively by scanning of a delay line. The system requires a scanning range of only a few millimeters to obtain multiple ring-down interferograms. In a proof-of-concept demonstration, the intrinsic losses of two loops are estimated. The measured combined-loss of both loops is compared to the sum of the loop losses measured separately with a conventional fiber-loop ring-down system. The result obtained using the proposed system exhibits a difference of only 0.06 dB with that of the reference system.