cuFFS (CUDA-accelerated Fast Faraday Synthesis) performs Faraday rotation measure synthesis; it is particularly well-suited for performing RM synthesis on large datasets. Compared to a fast single-threaded and vectorized CPU implementation, depending on the structure and format of the data cubes, cuFFs achieves an increase in speed of up to two orders of magnitude. The code assumes that the pixels values are IEEE single precision floating points (BITPIX=-32), and the input cubes must have 3 axes (2 spatial dimensions and 1 frequency axis) with frequency axis as NAXIS1. A package is included to reformat data with individual stokes Q and U channel maps to the required format. The code supports both the HDFITS format and the standard FITS format, and is written in C with GPU-acceleration achieved using Nvidia's CUDA parallel computing platform.