We apply an intensity-modulation technique to dual-comb spectroscopy to improve its detection sensitivity. The scheme is demonstrated via Doppler-free optical–optical double-resonance spectroscopy of Rb by modulating the intensity of a pump laser with frequencies set at rates 3 times lower and 50,000 times higher than the difference in the repetition rates of the two frequency combs. The signal-to-noise ratios are enhanced by 3 and 6 times for slow and fast modulations, respectively, compared to those of conventional dual-comb spectroscopy without any intensity modulation. The technique is widely applicable to pump-probe spectroscopy with dual-comb spectroscopy and provides high detection sensitivity.