At Auscrypt'92, Harn and Yang first proposed the conception of (t,n) threshold undeniable signature, in which only subsets with at least t members can represent a group to generate, confirm or disavow a signature. Later, several schemes are proposed, but none of them is secure. So up to now, how to design a secure (t,n) threshold undeniable signature scheme is remained an open problem. In this paper, based on discrete logarithm cryptosystem, a secure and efficient (t,n) threshold undeniable signature scheme without a trusted party is presented. This scheme has an attractive property that member's honesty is verifiable because a publicly verifiable secret sharing scheme is used to distribute secrets and two discrete logarithm equality protocols are used to provide necessary proofs of correctness, which are proposed by Schoenmakers at Crypto'99.