A low-complexity complex-valued sliding discrete cosine transform least-mean square（DCT-LMS） adaptive algorithm and its realization structure on field programmable gate array（FPGA） are researched.A revised sliding DCT is added in input port of conventional LMS algorithm to guarantee a fast convergence rate when relevance of input signals are reduced.The revised sliding DCT algorithm is optimized to improve stability and precision in hardware realization.The realization structure

result and the comparison with Matlab simulation result are presented.The resource utilization of the algorithm in FPGA is analyzed.The algorithm has been successfully used in practical engineering and its effect is better than conventional LMS adaptive algorithm.