Secret sharing and digital signature is an important research area in information security and has wide applications in such fields as safeguarding and legal use of confidential information, secure multiparty computation and electronic commerce. But up to now, study of signature based on general vector space secret sharing is very weak. Aiming at this drawback, the authors did some research on vector space secret sharing against cheaters, and proposed an efficient but secure vector space secret sharing based multi-signature scheme, which is implemented in two channels. In this scheme, the group signature can be easily produced if an authorized subset of participants pool their secret shadows and it is impossible for them to generate a group signature if an unauthorized subset of participants pool their secret shadows. The validity of the group signature can be verified by means of verification equations. A group signature of authorized subset of participants cannot be impersonated by any other set of participants. Moreover, the suspected forgery can be traced, and the malicious participants can be detected in the scheme. None of several possible attacks can successfully break this scheme.