Abstract: Signcryption is a public key cryptographic primitive that combines the functionalities of encryption and digital signature in a single logical step with low-overhead computation and communication. Some secure problems are found in the existing multi-receiver signcryption scheme, that is, disclosure of the recipients' privacy, unfair de-signcryption and no public verifiability. In order to solve these problems, a new identity-based multi-receiver signcryption scheme is presented by using Lagrange interpolating polynomial in this paper. The proposed scheme has three major features: the anonymous de-signcryption which can protect the recipients' privacy by gathering identity information of all the authorized recipients, the fair de-signcryption which means the same ciphertexts are received by all the authorized recipients, and the public verifiability which ensures that any third parties are able to verify the validity of the sender by the ciphertext only. Moreover, the signer only needs to compute one bilinear paring operation and one exponent operation in the implementation of the proposed scheme. Compared with the existing signcryption schemes, the proposed scheme is more efficient in the computational complexity and ciphertext size. Finally, we prove its semantic security under the hardness of bilinear Diffie-Hellman (BDH) problem and its unforgeability under the computational Diffie-Hellman (CDH) assumption in the random oracle model respectively.