For most present threshold signature schemes, sub-sign member can not sign a message anonymously or theirs anonymity is very weak. To improve their anonymity, a strong anonymity (n, t) threshold signature scheme based on DAA (Direct Anonymous Attestation), which is adopted by Trusted Computing Group v1.2 specifications, is proposed. Compared with the others, the scheme colligates DAA, zero-knowledge proof and Feldman verifiable secret sharing technique to achieve untraceable sub-sign and insure strong anonymity of signers, even the verifier and the dealer are colluded. Besides strong anonymity, analysis shows the scheme also has the property of unforgeable share, verifiable sub-sign, and robustness etc. It can be used in the situations which desire high-level anonymity such as anonymous voting.