Nowadays, a large number of groups choose to deploy their applications to cloud platforms, especially for the big data era. Currently, the hybrid cloud is one of the most popular computing paradigms for holding the privacy-aware applications driven by the requirements of privacy protection and cost saving. However, it is still a challenge to realize data placement considering both the energy consumption in private cloud and the cost for renting the public cloud services. In view of this challenge, a cost and energy aware data placement method, named CEDP, for privacy-aware applications over big data in hybrid cloud is proposed. Technically, formalized analysis of cost, access time, and energy consumption is conducted in the hybrid cloud environment. Then a corresponding data placement method is designed to accomplish the cost saving for renting the public cloud services and energy savings for task execution within the private cloud platforms. Experimental evaluations validate the efficiency and effectiveness of our proposed method.