The traditional threshold signature scheme is a combination of the digital signature scheme and the secret sharing scheme. Any group of t (threshold value) or more players can reconstruct the secret together but no group of fewer than t players can in secret sharing scheme. Because of this property of secret sharing scheme, the current threshold signature scheme has a natural weakness in the anti-collusion attack. A new threshold signature scheme based on the factorial decompose theorem is designed successfully without the secret sharing scheme in order to get the ability of anti-collusion attacks. It not only has the property of group signature and threshold signature, but also has some good features including traceability，robustness and resisting forgery attacks.