Group undeniable signatures are like ordinary group signatures except that verifying signatures needs the help of the group manager. In this paper, we propose a convertible group undeniable signature scheme in which the group manager can turn all or selective signatures, which are originally group undeniable signatures, into ordinary group signatures without compromising security of the secret key needed to generate signatures. The proposed scheme also allows the group manager to delegate the ability to confirm and deny to a limited set of parties without providing them the capability of generating signatures. For business applications, convertible group undeniable signatures can be widely used to validate price lists, press release or digital contracts when the signatures are commercially sensitive or valuable to a competitor. Our scheme is unforgeable, signature-simulatable and coalition-resistant. The confirmation and denial protocols are also zero-knowledge. Furthermore, the time, space and communication complexity are independent of the group size.