The chosen-ciphertext attack (CCA) security model can effectively figure active attacks in reality. The existing cryptosystems against CCA are mainly designed by foreign countries, and China is lack of its CCA secure cryptosystems. Although there are general transformation approaches to achieving CCA security, they lead to an increase in both computational overhead and communication overhead. Based on the SM9 encryption algorithm, this study proposes an identity-based broadcast encryption scheme with CCA security. The design is derived from the SM9, and the size of the private key and ciphertext is constant and independent of the number of receivers chosen in the data encryption phase. Specifically, the private key includes one element, and the ciphertext is composed of three elements. If the GDDHE assumption holds, the study proves that the proposed scheme has selective CCA security under the random oracle model. In order to achieve CCA security, a dummy identity is introduced in designing the encryption algorithm, and the identity can be used to answer the decryption query successfully. Analysis shows that the proposed scheme is comparable to the existing efficient identity-based broadcast encryption schemes in terms of computational efficiency and storage efficiency.