We found that an acoustically-induced perturbation can support a different type of quasi-phase matching for nonlinear frequency conversions in gas-filled hollow-core photonic crystal fibers. A gas pressure grating, a periodic spatial modulation of gas pressure, which is reversibly constructed by the acoustically-induced perturbation, compensates a nonzero phase mismatch and enhances the nonlinear optical process. The field amplitude oscillates about the averaged field amplitude which lineally grows with distance. While group velocity walk-off is suppressed by manipulating the gas pressure inside the fiber, a nonzero wavevector mismatch is inevitable, which can be compensated by the acoustically-induced perturbation. The frequency conversion is switchable by turning on/off the acoustically-induced perturbation. We exemplarily consider third-harmonic generation in gas-filled hollow-core photonic crystal fibers, however the conception of acoustically-induced quasi-phase matching is applicable to other kinds of nonlinear optical processes in gas-filled structures such including four-wave mixing and sum frequency generation and it would provide a new route for nonlinear optics and acoustooptics.