Most of the existing Ciphertext-Policy Attribute-Based Encryption (CP-ABE) schemes cannot support multi-state representation of attributes, and the computation overhead of encryption and decryption phase is huge. In order to solve the problems, a CP-ABE scheme with Weighted Attribute Revocation (CPABEWAR) was proposed. On the one hand, the expression ability of attribute was improved by introducing the concept of weighted attribute. On the other hand, in order to reduce the computation cost, part calculation tasks were outsourced to Cloud Service Provider (CSP) under the premise of ensuring data securer. The analysis results show that, the proposed CPABEWAR is proved to be Chosen Plaintext Secure (CPS) under the Decisional Bilinear Diffie-Hellman (DBDH) assumption. The proposed scheme simplifies the access tree structure at the cost of a small amount of storage space and improves system efficiency and flexibility of access control, which is suitable for cloud users with limited computing power.