Recently, M. Sekhar gave a digital signature scheme with message recovery, where only a specific verifier can directly check the validity of the signature. A third party can distinguish a valid signature through a zero-knowledge proof protocol. However we find that the proposed scheme is in-secure. A forgery attack strategy on M. Sekhar's scheme has been designed; anyone who has a valid signature can forge a signature on an arbitrary message. An improved signature scheme, which can resist the forgery attack and a zero-knowledge proof protocol with which a third party can distinguish a valid signature are presented. Also,the security of the improved scheme is analyzed.