To solve the problem of high preprocessing cost and public verifiability in the verifiable outsourced database schemes, a publicly verifiable outsourced database with full delegation is proposed. The architecture and the definition of security and correctness of the model are present. Based on the bilinear map and verifiable outsourced modular exponentiations protocol, a publicly verifiable outsourced database scheme with full delegation is constructed, and each algorithm is designed in detail. The rigorous security proof is presented under the bilinear Diffie-Hellman exponent (BDHE) problem. Compared with performing the protocol without full delegation scheme and the existing schemes, the data owner in publicly verifiable outsourced database with full delegations scheme outsources more operations to the cloud because of the application of the verifiable outsourced modular exponentiation operation. The theoretical analysis and simulation confirm that the cost of the proposed scheme is lower in the preprocessing phase, which makes it more efficient and practical. In the verification phase, any user can verify the result since the verification algorithm does not take any secret key as input. Therefore, the proposed scheme achieves public verifiability.