Privacy-preserving profile matching, a challenging task in mobile social networks, is getting more attention in recent years. In this paper, we propose a novel scheme that is based on ciphertext-policy attribute-based encryption to tackle this problem. In our scheme, a user can submit a preference-profile and search for users with matching-profile in decentralized mobile social networks. In this process, no participant's profile and the submitted preference-profile is exposed. Meanwhile, a secure communication channel can be established between the pair of successfully matched users. In contrast to existing related schemes which are mainly based on the secure multi-party computation, our scheme can provide verifiability (both the initiator and any unmatched user cannot cheat each other to pretend to be matched), and requires few interactions among users. We provide thorough security analysis and performance evaluation on our scheme, and show its advantages in terms of security, efficiency and usability over state-of-the-art schemes.