Verifiable multi-secret sharing on general access structures was studied.A method of construct verifiable se-cret sharing schemes with arbitrary access structure was given.The verifiable multi-secret sharing schemes constructed by this method have the following properties: multiple secrets can be shared at the same time in a group of shareholders.The secret shares sent to shareholders are publicly verifiable.The public information with respect to each shared secret is publicly verifiable.And the supply of false shares in the process of secret recovery can be prevented.Analysis shows that the verifiable multi-secret sharing schemes constructed by our method are not only secure

but also efficient.