This paper introduces a new concept of convertible user designating confirmer partially blind signature, in which only the designated confirmer (designated by the user) and the user can verify and confirm the validity of given signatures and convert given signatures into publicly verifiable ones. We give a formal definition for it and propose a concrete provably secure scheme with a proof of security and a brief analysis of efficiency. Assuming the intractabilities of the Discrete Logarithm Problem and the ROS-Problem, the proposed scheme is unforgeable under adaptive chosen-message attack.