Public key encryption with equality test (PKE-ET) enables anyone to perform equivalence test between two messages encrypted under distinct public keys. Attribute-hiding predicate encryption is a paradigm for public key encryption that supports both attribute-hiding and fine-grained access control. In this paper, we first initialize the concept of attribute-hiding predicate encryption with equality test (AH-PE-ET) by incorporating the notions of PKE-ET and PE, and then propose a concrete AH-PE-ET scheme. Inheriting the merits of predicate encryption, versatile access control can be achieved such that the ciphertexts and the secret key are, respectively, associated with the descriptive attributes x and the boolean functions f and decryption can only be done iff(x) returns true. In the AH-PE-ET scheme, one data receiver can calculate a trapdoor using his/her private key and delivers this trapdoor to an untrusted cloud server, who in turn compares the ciphertexts from this receiver with other receivers' ciphertexts. During the comparison, the information about the trapdoor as well as the attributes associated with the ciphertexts will not be disclosed to this cloud server. Furthermore, it is also proven to be selectively secure against the chosen plaintext attack in the standard model under the decisional bilinear Diffie-Hellman assumption. Finally, the theoretical performance analysis and experimental simulation indicate the feasibility and practicability of our suggested scheme.