Dual-comb systems generated from a single cavity are compelling options for scientific and technical applications, owing to the naturally high coherence in the same cavity. We reported on a multiplexed dual-comb system in a bidirectional mode-locked fiber laser based on carbon nanotubes. A pair of frequency combs with different repetition rates in opposite directions was achieved at the 1.5-μm band simultaneously, composing a single-cavity dual-comb system. The repetition rate was 9.99 MHz and the repetition rate difference was tunable from 9 to 24 Hz. The overlapped spectra of two combs enabled simple dual-comb spectroscopy, where the spectrum with wide bandwidth up to 8 nm was mapped to the frequency domain of interferograms without correction or post-signal process. The multiplexed dual-comb system was realized by increasing the pump power and tuning the polarization state. The two beat notes generated in one interference period could both map spectral information. Such kind of multiplexed dual-comb system offers a novel tool for studying the spectral evolution of solitons and optimizing channel-multiplexed applications.