Cipher-policy attribute-based encryption (CP-ABE) is a more efficient and flexible encryption system as the encryptor can control the access structure when encrypting a message. In this paper, we propose a privacy-preserving decentralized CP-ABE (PPDCP-ABE) scheme where the central authority is not required, namely each authority can work independently without the cooperation to initialize the system. Meanwhile, a user can obtain secret keys from multiple authorities without releasing his global identifier (GID) and attributes to them. This is contrasted to the previous privacy-preserving multi-authority ABE (PPMA-ABE) schemes where a user can obtain secret keys from multiple authorities with them knowing his attributes and a central authority is required. However, some sensitive attributes can also release the user's identity information. Hence, contemporary PPMA-ABE schemes cannot fully protect users' privacy as multiple authorities can cooperate to identifier a user by collecting and analyzing his attributes. Therefore, it remains a challenging and important work to construct a PPMA-ABE scheme where the central authority is not required and both the identifiers and the attributes are considered. © 2014 Springer International Publishing Switzerland.