A method is proposed for compressing laser pulses by fast-extending plasma gratings (FEPGs), which are created by ionizing a hypersonic wave generated by stimulated Brillouin scattering in a background gas. Ionized by a short laser pulse, the phonon forms a light-velocity FEPG to fully reflect a resonant pump laser. As the reflecting surface moves with the velocity of light, the reflected pulse is temporally overlapped and compressed. One- and two-dimensional fully kinetic particle-in-cell simulations with a laser wavelength of 1 µm show that in this regime, a pump pulse is compressed from 10–40 ps to 7–10 fs (i.e., a few optical cycles), with a two-dimensional transfer efficiency up to 60%. This method is a promising way to produce critical laser powers while avoiding several significant problems that arise in plasma-based compressors, including an unwanted linear stage, major plasma instabilities, and the need for seed preparation.