In the undeniable signatures, the validity or invalidity can only be verified via the Confirmation/Disavowal protocol with the help of the signer. Convertible undeniable signatures provide the flexibility that a signer can convert an undeniable signature into publicly verifiable one. A proxy signature scheme allows an entity to delegate his/her signing capability to another entity in such a way that the latter can sign messages on behalf of the former when the former is not available. Proxy signatures have found numerous practical applications in ubiquitous computing, distributed systems, mobile agent applications, etc. In this paper, we propose the first convertible undeniable proxy signature scheme with rigorously proven security. The properties of Unforgeability, Invisibility and Soundness in the context of convertible undeniable proxy signatures are also clearly defined. The security of our construction is formally proven in the random oracle models, based on some natural complexity assumptions.