Aimed at the problem that the security of some multi-secret sharing schemes only depends on a single coefficient, and based on the bilinear pairings and the Shamir threshold scheme, this paper proposes a public verifiable secret scheme. In the scheme, the secret key computation of participant is apart from the process of secret distribution. The secret key is chosen by the participant himself and the participant only needs to keep one secret key. By so doing the multi- secrets sharing at will in the process can be realized. The public verifiable scheme is effectively applied in the process of the secret distribution and the secret recovery ,so that anyone could be able to verify the correctness of the share to effectively prevent the dishonest participant and the dealer from cheating. The dealer and the participant transmit information through the public channel rather than the secret channel, thus reducing the system costs. The sharing of multi-secret lies in multiple coefficients, and the leak of a single coefficient or secret does not lead to the leak of other secrets. By using the Elliptic Curve Discrete Logarithm Problem and Bilinear Diffie-Hellman Problem, the security of the scheme is guaranteed. At last, mathematical proof and theoretical analysis of validity and expansion of the scheme are given.