In the (t,n) proxy signature scheme, the signature, originally signed by a signer, can be signed by t or more proxy signers out of a proxy group of n members. Recently, an efficient nonrepudiable threshold proxy signature scheme with known signers was proposed by H.-M. Sun. Sun's scheme has two advantages. One is nonrepudiation. The proxy group cannot deny that having signed the proxy signature. Any verifier can identify the proxy group as a real signer. The other is identifiable signers. The verifier is able to identify the actual signers in the proxy group. Also, the signers cannot deny that having generated the proxy signature. In this article, we present a cryptanalysis of the Sun's scheme. Further, we propose a secure, nonrepudiable and known signers threshold proxy signature scheme which remedies the weakness of the Sun's scheme.