Fourier single-pixel imaging (FSI) allows an image to be reconstructed by acquiring the Fourier spectrum of the image using a single-pixel detector. Fast FSI is typically achieved by acquiring a truncated Fourier spectrum, that is, only low-frequency Fourier coefficients are acquired, with the high-frequency coefficients discarded. However, the truncation of the Fourier spectrum leads to undesirable ringing artifacts in the resulting image. Ringing artifacts produce false edges in the image and reduce the image contrast, resulting in image quality degeneration. The artifact is particularly severe in dynamic FSI, where the sampling ratio is generally ultra-low. We propose an effective and fast deringing algorithm to achieve ringing-free fast FSI. The algorithm eliminates ringing artifacts through 2D sub-pixel shifting and preserves image details through image fusion. Both static and dynamic imaging results demonstrate that the proposed method can reconstruct ringing-free images from under-sampled data in FSI. The deringing algorithm not only provides FSI with the capability of fast high-quality single-pixel imaging but also might prove its applicability in other areas, such as Fourier-based data compression algorithms.