In this study, we propose a pioneering spatially frequency-shifted super-resolution microscopy technique that utilizes the synergy of quasiperiodic gratings and deep learning. First, a quasiperiodic grating capable of converting evanescent waves into propagating waves is designed. The grating is positioned between the object under investigation and the objective lens, and the high-frequency information carried by the evanescent waves in the near-field region of the object is shifted into the detection window and becomes accessible in the far field for imaging. Subsequently, we provide two deep learning models for image and video reconstructions to achieve the reconstruction of static and dynamic samples respectively. Simulation results demonstrate the high feasibility of the proposed method, and both static and dynamic objects with sub-wavelength features can be resolved. The developed method paves the way to the realization of super-resolution imaging by using a traditional bright-field microscope without the need for an extensive optical system design.