Traceable ring signatures, proposed at PKC'07, are a variant of ring signatures, which allow a signer to anonymously sign a message with a tag behind a ring, i.e., a group of users chosen by the signer, unless he signs two messages with the same tag. However, if a signer signs twice on the same tag, the two signatures will be linked and the identity of the signer will be revealed when the two signed messages are different. Traceable ring signatures can be applied to anonymous write-in voting without any special voting authority and electronic coupon services. The previous traceable ring signature scheme relies on random oracles at its security and the signature size is linear in the number of ring members. This paper proposes the first secure traceable ring signature schemes without random oracles in the common reference string model. In addition, the proposed schemes have a signature size of O(√N), where N is the number of users in the ring.