Focusing on the deficiencies on performance and security of the existing anonymous broadcast encryption scheme, a new anonymous broadcast encryption scheme based on the Lagrange interpolation polynomial was proposed. Firstly, an anonymous broadcast encryption security model against adaptive adversaries was defined. Then the scheme was constructed based on the Lagrange interpolation polynomial under the composite order bilinear group settings, which ensures user identity anonymity and achieves an efficient encryption and decryption at the same time. Finally, based on the subgroup decision assumption and the composite decisional bilinear Diffie-Hellman assumption, the security was proved in standard model, which shows that the proposed scheme has both ciphertext confidentiality and receiver anonymity against adaptive adversaries. Experimental results and performance analysis show that the proposed method has low communication and computing overhead, and can efficiently solve the anonymous access control issues of ciphertext data in cloud storage.