Abstract: In Ciphertext-Policy Attribute-Based Encryption (CP-ABE), some attributes in the access policy may disclose privacy or sensitive information. Therefore, a multi-authority CP-ABE scheme with obfuscated sensitive attributes is proposed. According to the correlation between attributes and sensitive information, the scheme divides attributed into three categories: global sensitive, local sensitive and general. Sensitive attributes in access policies during encryption were obfuscate, and the non-sensitive attributes remained in a plain-text format. Two attribute authorities cooperated to predict the user's decryption ability to avoid useless decryption attempts. Thus, we could not only prevent revealing sensitive information but also reduce the time and space cost of encryption and decryption by keeping the non-sensitive attributes public, consequently achieving a better tradeoff between policy confidentiality and the efficiency of the cryptosystem.