After a comparison of the speed of Berlekamp-Massey(BM) algorithm to that of Euclidean algorithm,BM algorithm is selected to design a reed-solmon(RS) decoder,whose can reach 36 Mbps.Furthermore,according to the data transfer rate(DTR) of third generation discs,this paper analyzes the minimum speed for RS decoding and simulates the finite field multiplier in RS decoding.Operating at clock speed of 50 MHz in FPGA,the multiplier can meet the demand of DTR.