We report the mechanism and modeling for the two-dimensional shock-induced instability of a dual-layer gas-particle mixture. In the mixture, the instability is triggered by the pressure perturbation near the perturbed interface instead of the baroclinic vorticity. The velocity difference of gas induced by the pressure perturbation drives the particle interface to grow via drag coupling effects. Inspired by this interfacial instability mechanism, we estimate the growth of the particle interface in the linear stage.