Public-key Authenticated Encryption with Keyword Search (PAEKS) is a cryptographic primitive that can resist inside keyword guessing attack (KGA). However, most of the previously proposed PAEKS frameworks suffered from certificate management problem and key escrow problem. Inspired by the ideas of certificate-based cryptography, we propose a secure-channel free certificateless searchable public key authenticated encryption with keyword search (SCF-CLPAEKS) scheme which sloves the key escrow problem in identity-based cryptosystems and the cumbersome certificate problem in conventional public key cryptosystems. Our scheme achieves security against keyword guessing attacks are performed by both inside and outside adversaries. Moreover, our scheme satisfies ciphertext indistinguishability (CI), trapdoor indistinguishability (TI), and designated testability simultaneously. The comparisons indicate that our SCF-CLPAEKS scheme enjoys a better performance compared with related schemes.