Threshold blind signature is playing an important role in cryptography as well as in practical applications such as e-cash and e-voting systems, etc. In this paper, we present an efficient and practical threshold bind signature from Weil pairing on super-singular elliptic curves or hyper-elliptic curves over finite field and prove that our scheme is provably secure in the random oracle model. Threshold blind signature is playing an important role in cryptography as well as in practical applications such as e-cash and e-voting systems, etc. In this paper, we present an efficient and practical threshold bind signature from Weil pairing on super-singular elliptic curves or hyper-elliptic curves over finite field and prove that our scheme is provably secure in the random oracle model.