An optomechanical cavity embedded with a V-type three-level atom is exploited to control single-photon transport in a one-dimensional waveguide. The effects of the atom–cavity detuning, the optomechanical effect, the coupling strengths between the cavity and the atom or the waveguide, and the atomic dissipation on the single-photon transport properties are analyzed systematically. Interestingly, the single-photon transmission spectra show multiple double electromagnetically induced transparency. Moreover, the double electromagnetically induced transparency can be switched to a single one by tuning the atom–cavity detuning.