Binary Goppa codes are a large and powerful family of error-correcting codes. But how tofind the true minimum distance of binary Goppa codes is not solved yet. In this paper a new lowerbound for the minimum distance of binary Goppa codes is shown. This new lower bound improvesthe results in Y. Sugiyama (1976) and Fang Guiliang’s (1983) papers. The method in this paper canbe generalized to other Goppa codes easily.