Proxy re-encryption (PRE) is a cryptographic primitive introduced by Blaze, Bleumer and Strauss  to provide delegation of decryption rights. PRE allows re-encryption of a ciphertext intended for Alice (delegator) to a ciphertext for Bob (delegatee) via a semi-honest proxy, who should not learn anything about the underlying message. In 2003, Al-Riyami and Patterson introduced the notion of certificateless public key cryptography which offers the advantage of identity-based cryptography without suffering from key escrow problem. The existing certificateless PRE (CLPRE) schemes rely on costly bilinear pairing operations. In ACM ASIA-CCS SCC 2015, Srinivasan et al. proposed the first construction of a certificateless PRE scheme without resorting to pairing in the random oracle model. In this work, we demonstrate a flaw in the CCA-security proof of their scheme. Also, we present the first construction of a CLPRE scheme without pairing which meets CCA security under the computational Diffie-Hellman hardness assumption in the random oracle model. © 2017, Springer International Publishing AG.