An optical setup and corresponding reconstruction algorithm are proposed to realize single-shot Fourier ptychography (FP). Multiple angle-varied object waves are generated by placing a Dammann grating at a certain distance behind the object, and the generated image array of low resolution corresponding to different diffraction orders formed on the detector plane is recorded simultaneously in a single exposure. The amplitude, as well as the phase information of the object, can be properly reconstructed with a common FP algorithm from the recorded image array. This method eliminates the requirement for the angular scanning of common FP, and the total acquisition time is dramatically reduced. The feasibility of this proposed method was demonstrated both numerically and experimentally. The proposed method has the advantages of fast data acquisition and corresponding high temporal resolution, making it very suitable for applications in which high imaging speed is required.