We present a superresolution imaging method based on the dynamic single-pixel compressive sensing (CS) system. Different from the traditional static CS, this system is slowly moving in parallel with the scene during the compressive sampling, implying that the measurements are possible to contain the information about the scene with the subpixel resolution. Here we first build the dynamic compressive sampling model and give the recovery method via traditional CS scheme, and then we propose the image superresolution recovery method in the CS framework, where a subdivision scheme is used. The proposed method not only has remarkable superresolution performance, but also has low requirements on the imaging system, since it is associated with the single-pixel imager, which is one of the simplest systems in the existing CS imaging architectures. The feasibility of the proposed method is demonstrated by the numerical simulations as well as the optical experiments.