Dual-comb spectroscopy utilizes two sets of comb lines with slightly different comb-tooth-spacings, and optical spectral information is acquired by measuring the radio-frequency beat notes between the sets of comb lines. It holds the promise as a real-time, high-resolution analytical spectroscopy tool for a range of applications. However, the stringent requirement on the coherence between comb lines from two separate lasers and the sophisticated control system to achieve that have confined the technology to the top metrology laboratories. By replacing control electronics with an all-optical dualcomb lasing scheme, a simplified dual-comb spectroscopy scheme is demonstrated using just one dual-wavelength, passively mode-locked fiber laser.Dual-comb pulses with a repetition-frequency difference determined by the intracavity dispersion are shown to be sufficiently stable against common-mode cavity drifts and noises. As sufficiently low relative linewidth is maintained between two sets of comb lines, capability to resolve RF beat notes between comb teeth and picometer-wide optical spectral features is demonstrated using a simple data acquisition and processing system in an all-fiber setup. Possibility to use energy-efficient, free-running fiber lasers with a small comb-toothspacing could enable the realization of low-cost dual-comb spectroscopy systems affordable to more applications.