Universal designated verifier signature schemes allows a signature holder to designate the signature to a desire designated verifier, in such a way that only designated verifier can verify this signature, but is unable to convince anyone else of this fact.The previous constructions of universal designated verifier signature rely on the underlying public key infrastructure, that needs both signers and verifiers to verify the authenticity of the public keys, and hence, the certificates are required.This article presents the first model and construction of the certificateless universal designated verifier signature scheme, in which the certificates are not needed.The proposed scheme satisfies all the requirements of the universal designated verifier signature in the certificateless system.Security proofs are provided for the scheme based on the random oracle model, assuming that the Bilinear diffie-hellman (BDH) problem is hard to solve.