The drawback of the first asynchronous proactive RSA scheme presented by Zhou in 2001, is that the security definition and security proof do not follow the approach of provable security. This paper presented a provably secure asynchronous proactive RSA scheme, which includes three protocols: initial key distribution protocol, signature generation protocol and share refreshing protocol. Taken these protocols together, a complete provably secure proactive RSA scheme was obtained. And the efficiency of the scheme is approximate to that of the scheme of Zhou. The drawback of the first asynchronous proactive RSA scheme presented by Zhou in 2001, is that the security definition and security proof do not follow the approach of provable security. This paper presents a provably secure asynchronous proactive RSA scheme, which includes three protocols: initial key distribution protocol, signature generation protocol and share refreshing protocol. Taken these protocols together, a complete provably secure proactive RSA scheme was obtained. And the efficiency of the scheme is approximate to that of the scheme of Zhou.