A non-interactive verifiable secret redistribution protocol based on additive sharing is put forward, which has threshold attribute, too. It can be applied to all the sets of shareholders that can alter the access structure, so the set of new shareholders doesn't need to joint the one of old shareholders. The protocol adopts additive sharing and share back-up technologies, so it can not only verify the correctness of secret shares and subshares, but also recovery bad secret shares. In addition, it can resolve the hard problem of how to identify the set of bad shareholders. It can be transformed into redistribution protocol in proactive RSA conveniently thanks to additive sharing. The protocol is correct, robust and secure, and its performance in many aspects is very high.