This paper extends the concept of partially blind signature to the convertible undeniable partially blind signature, in which only the signer can verify and confirm the validity of given signatures and convert given signatures into universally verifiable signatures, along with a formal definition for it and a practical scheme that implements it. The proposed scheme is efficient and secure, in which its unforgeability is the same as that of the Schnorr's signature scheme and its untransferability relies on the hardness of decision Diffie-Hellman problem.