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A publicly verifiable secret sharing allows anyone to detect the cheating of dealer or participants only from the public information. In order to expand the application scope of multi-secret sharing, firstly, a publicly verifiable multi-stage secret sharing (PVMSSS) scheme is proposed, and then based on the monotone span program (MSP) and secure multi-party computation, a renewable multi-stage secret sharing scheme that can be publicly verified and used in general access structures is proposed. In the secret distribution stage, the secret share of the participants in the scheme is calculated by each participant, and the dealer does not need to transmit any secret information to the participants. Moreover, each participant only needs to maintain one secret share to realize the reconstruction of multiple secrets. Using bilinear pairing properties, anyone can verify the correctness of the secret shares before and after the update and the validity of the public information, thereby effectively preventing fraud by dealer and participants. In the secret reconstruction phase, the pseudo-share is constructed by using secure multi-party computation to ensure that the real share of each participant will never be exposed, and the versatility of the scheme is realized. In each update of the secret, the dealer only needs to announce the related public information of updated temporary shares to update the participants' secret share. Finally, the correctness and security of the scheme are analyzed. Analysis shows that under the computational Diffie-Hellman and decisional bilinear Diffie-Hellman problems and assumptions, the proposed scheme is provably secure.