In the cloud era people get used to store their data to the cloud server, and would use encryption technique to protect their sensitive data from leakage. However, encrypted data management is a challenging problem, for example, encrypted data classification. Besides, how to effectively control the access to the encrypted data is also an important problem. Ciphertext-policy attribute-based encryption with equality test (CP-ABEET) is an efficient solution to the aforementioned problems, which enjoys the advantage of attribute-based encryption, and in the meanwhile supports the test of whether two different ciphertexts contain the same message without the need of decryption. However, the existing CP-ABEET schemes suffer from high computation costs. In this paper, we study how to outsource the heavy computation in CP-ABEET scheme to a third-party server. We introduce the notion of CP-ABEET supporting outsourced decryption (OCP-ABEET), which saves a lot of local computation loads of CP-ABEET. We propose a concrete construction of OCP-ABEET, and prove its security based on a reasonable number-theoretic assumption in the random oracle model. Compared with the existing CP-ABEET schemes, our scheme is more computationally efficient.