In proxy re-signature (PRS), a signature computed by Alice's secret key can be transferred to be a new signature by a proxy equipped with the re-signature key, while the new signature can be verified by Bob's public key. However, until now all the PRS scheme have this feature: the proxy can transfer all the delegatee's signature to be the delegator's one, which sometimes in practical applications is undesirable. Thus in this paper, we propose the notion of proxy re-signature supporting conditional delegation (or conditional proxy re-signature). Here we emphasis that, although there exist the concept of conditional proxy re-encryption (CPRE), our idea is not directly adapting the technique of CPRE to the signature setting. In our CPRS scheme, the delegatee need not to change its own signature algorithm to support the conditional delegation, thus it is more friendly to the existing signature system.