Public-key encryption has been generalized to adapt to more and more practical applications. Broadcast encryption, introduced by Fiat and Naor in 1993, aims for applications in pay-TV or satellite transmission and allows a sender to securely send private messages to any subset of users, the target set. Sahai and Waters introduced Attribute-based Encryption (ABE) to define the target set in a more structural way via access policies on attributes. Attribute-based Broadcast Encryption (ABBE) combines the functionalities of both in an efficient way. In the relevant applications such as pay-TV, the users are given a relatively small device with very limited secure memory in a smartcard. Therefore, it is of high interest to construct schemes with compact secret key of users. Even though extensively studied in the recent years, it is still an open question of constructing an efficient ABBE with constant-size private keys for general forms of access policy such as CNF or DNF forms. This question was partially solved at ESORICS '15 where Phuong \emph{et al.} introduced a constant secret-key size ABBE. But they manage restrictive access policies only supporting AND-gates and wildcards. In this paper, we solve this open question and propose an efficient constant-size private key ciphertext-policy attribute-based broadcast encryption scheme for DNF form. In particular, we also present the optimization in implementing our proposed scheme.