Attribute-based signature (ABS) is a versatile and useful cryptogrammic technology. In an ABS scheme, every signer is distributed a signing secret key in term of her/his attributes, and endorses a message in relation to some signing policy fulfilled by the signer's attributes. The verifier checks that the signature is indeed endorsed by the signer whose attributes match with the signing policy. However, existing ABS schemes suffer from the issue of abusing signature and key exposure. To address the above issues, we provide a traceable and forward-secure attribute-based signature (TFS-ABS) scheme with constant-size supporting flexible threshold predicates. Furthermore, we prove that the presented TFS-ABS scheme is existential unforgeability against selective predicate attack under the standard model. We reduce the security for the provided scheme to$q$-Diffie-Hellman exponentiation assumption. The designed scheme can be used to alleviate the damage induced by key exposure and traces the real identity of signer by attribute authority (AA) when the signer occurs abusing behavior. Furthermore, the signature size in presented scheme keeps constant and is independent of the number of attributes. Experimental evaluations exhibit that the presented TFS-ABS scheme is efficient in term of the communication and computation overhead.