As an important step in the post-processing part of quantum communication, the privacy amplification process can realize unconditional security of quantum key distribution (QKD) system by eliminating information leakage that may occur in the process of QKD. To reduce the consumption of hardware resources and improve the bandwidth of secure key rate, a high-speed privacy amplification algorithm based on cellular automata is implemented in this work using field programmable gate arrays (FPGA). Compared to the Toeplitz matrix scheme that requires huge matrix multiplication, this scheme has greater advantages in speed by improving the algorithm in line with the characteristics of FPGA hardware and pipeline structure. In the case of real-time transmission of reconciliation keys, this scheme can adapt to any length of input keys and any fractional compression ratio between 0 and 1. In addition, the 256-order cellular automata is used in this scheme to process 1.28 Mbits input keys, and the maximum bandwidth of secure key rate can reach 1540 Mbits/s at a compression ratio of 0.5.