Broadband, high resolution, and rapid measurements of dual-comb spectroscopy (DCS) generate a large amount of data stream. We numerically demonstrate significant data compression of DCS spectra by using a compressive sensing technique. Our numerical simulation shows a compression rate of more than 100 with a 3% error in mole fraction estimation of mid-infrared (MIR) DCS of two molecular species in a broadband (~ 30 THz) and high resolution (~ 115 MHz) condition. We also numerically demonstrate a massively parallel MIR DCS spectrum of 10 different molecular species can be reconstructed with a compression rate of 10.5 with a transmittance error of 0.003 from the original spectrum.