Big data analytics and management often need to exploit the processing and storage power of cloud computing. It is obviously important to choose a cloud service with good quality. Meanwhile, users fear data leakage and loss of privacy if their sensitive data is processed in the cloud. In this paper, we propose a novel cloud service selection method, called PQsel, where a cloud service is estimated by colligating its capability of privacy protection (CoPP) and quality of service (QoS). Using a fuzzy comprehensive evaluation technique and AHP-based approach, we calculate the CoPP of each cloud service based on the CoPPs of security mechanisms covering the entire data life-cycle. Furthermore, QoS-driven approaches are introduced to support the privacy-aware cloud selection. An example analysis is given to prove the reasonableness of the proposed method. Comprehensive experiments have been conducted, which demonstrate the effectiveness of the proposed method.