A promising solution to protect data privacy in cloud storage services is known as ciphertext-policy attribute-based encryption (CP-ABE). However, in a traditional CP-ABE scheme, a ciphertext is bound with an explicit access structure, which may leak private information about the underlying plaintext in that anyone having access to the ciphertexts can tell the attributes of the privileged recipients by looking at the access structures. A notion called CP-ABE with partially hidden access structures [14, 15, 18, 19, 24] was put forth to address this problem, in which each attribute consists of an attribute name and an attribute value and the specific attribute values of an access structure are hidden in the ciphertext. However, previous CP-ABE schemes with partially hidden access structures only support access structures in AND gates, whereas a few other schemes supporting expressive access structures are computationally inefficient since they are built from bilinear pairings over the composite-order groups. In this paper, we focus on addressing this problem, and present an expressive CP-ABE scheme with partially hidden access structures in prime-order groups.