Attribute-based broadcast encryption ( ABBE) under continual auxiliary leakage-resilient ( CALR) model can enhance the security of the shared data in broadcasting system since CALR model brings the possibility of new leakage-resilient ( LR) guarantees. However, there are many shortcomings in the existing works, such as relying on the strong assumptions, low computational efficiency and large size of ciphertexts, etc. How to solve the trade-off between security and efficiency is a challenging problem at present. To solve these problems, this paper gives an ABBE scheme resisting continual auxiliary leakage ( CAL) attack. ABBE scheme achieves constant size ciphertexts, and the computational complexity of decryption only depends on the number of receivers instead of the maximum number of receivers of the system. Additionally, it achieves adaptive security in the standard model where the security is reduced to the general subgroup decision (GSD) assumptions (or called static assumptions in the subgroup). Furthermore, it can tolerate leakage on the master secret key and private key with continual auxiliary inputs. Performance analysis shows that the proposed scheme is more efficient and practical than the available schemes.