The Internet of Things technology has been used in a wide range of fields, ranging from industrial applications to individual lives. As a result, a massive amount of sensitive data is generated and transmitted by IoT devices. Those data may be accessed by a large number of complex users. Therefore, it is necessary to adopt an encryption scheme with access control to achieve more flexible and secure access to sensitive data. The Ciphertext Policy Attribute-Based Encryption (CP-ABE) can achieve access control while encrypting data can match the requirements mentioned above. However, the long ciphertext and the slow decryption operation makes it difficult to be used in most IoT devices which have limited memory size and computing capability. This paper proposes a modified CP-ABE scheme, which can implement the full security (adaptive security) under the access structure of AND gate. Moreover, the decryption overhead and the length of ciphertext are constant. Finally, the analysis and experiments prove the feasibility of our scheme.