Based on the properties of cyclic codes, a new decoding algorithm for burst-error-correction is proposed in this paper. This algorithm can effectively correct burst errors with length that approaches to n-k for (n,k) Reed-Solomon (RS) codes. Moreover, due to the use of error locations correlation within a burst, divisions are exempted from the decoding process, achieving a fast decoding algorithm with much less computational complexity compared with existing algorithms. It is shown that the proposed algorithm can be widely used in wireless communications, wireless digital broadcast systems, and so on.