Proxy re-encryption (PRE), formalized by Blaze et al. in 1998, allows a proxy entity to delegate the decryption right of a ciphertext from one party to another without obtaining the information of the plaintext. In recent years, many studies have explored how to construct PRE schemes that support fine-grained access control for complex application scenarios, such as identity-based PRE and attribute-based PRE. Besides, in order to achieve more flexible access control, the predicate proxy re-encryption (PPRE) is further studied. However, existing PPRE is restricted with the inner product predicate function. Therefore, how to realize the PPRE of arbitrary predicate function is still a problem to be solved. In this manuscript, we propose a secure generic construction of predicate proxy key re-encapsulation mechanism built from a “linear” predicate key encapsulation mechanism. Since the secure key encapsulation mechanism can be used as a building block to construct public key encryption, we can obtain a PPRE from our construction. As a result, the results open up new avenues for building more flexible and fine-grained PPRE.