Bellare et al. provided new definitions of anonymous signature and several constructions that meet the new definitions. They also presented a generic method to transform any standard signature scheme into an anonymous signature scheme by commitment functionality. Their generic transform yields anonymous signature schemes in the standard model. When applying this generic transform to Waters signature scheme, some additional communication overhead are incurred since one has to commit a long bit-string which is the concatenation of a standard signature and the corresponding public key. To address this efficiency issue, we directly transform Waters signature scheme into an efficient anonymous signature scheme. We prove that our construction meets the new definitions by use of code-based games.