With the development of cloud computing, more and more sensitive data are uploaded to cloud by companies or individuals, which brings forth new challenges for outsourced data security and privacy. Ciphertext-policy attribute-based encryption (CP-ABE) provides fine-grained access control of encrypted data in the cloud; in a CP-ABE scheme, an access structure, also referred to as ciphertext-policy, is sent along with a ciphertext explicitly, and anyone who obtains a ciphertext can know the access structure associated with the ciphertext. In certain applications, access structures contain very sensitive information and must be protected from everyone except the users whose private key attributes satisfy the access structures. In this paper, we propose a new model for CP-ABE with partially hidden access structure (See Figure 2). In our model, each attribute consists of two parts: an attribute name and its value; if the private key attributes of a user do not satisfy the access structure associated with a ciphertext, the specific attribute values of the access structure are hidden, while other information about the access structure is public. Based on the CP-ABE scheme proposed by Lewko and Waters recently, we then present a concrete construction of CP-ABE with partially hidden access structure and prove that it is fully secure in the standard model. In addition, we discuss how our new model can be employed to construct a privacy-preserving electronic medical record system in the cloud environment.