At first, an convertible ID-based two-party ring signature scheme is designed, in such a scheme, after releasing of a converting information by the real signer, a ring signature can be transformed into a standard signature which can be verified publicly. And then, based on this ring signature, a convertible perfect concurrent signature protocol is proposed. Different from a general concurrent signature, there is an extra procedure called "ACONVERT" in this protocol, which can transform the exchanged ring signature into a common form, so it realizes the fair exchange of signature. At last, the security of the protocol is analyzed.