The mammography is the first choice of breast cancer screening, which has proven to be the most effective screening method. An antiscatter grid is usually employed to enhance the contrast of image by absorbing unexpected scattered signals. However, the grid pattern casts shadows and grid artifacts, which severely degrade the image quality. To solve the problem, we propose the patch based frequency signal filtering for fast grid artifacts suppressing. As opposed to whole image processing synchronously, the proposed method divides image into a number of blocks for tuning filter simultaneously, which reduces the frequency interference among image blocks and saves computation time by multithread processing. Moreover, for mitigating grid artifacts more precisely, characteristic peak detection is employed in each block automatically, which can accurately identify the location of the antiscatter grid and its motion pattern. Qualitative and quantitative studies were performed on simulation and real machine data to validate the proposed method. The results show great potential for fast suppressing grid artifacts and generating high quality of digital mammography.