The key-exposure problem has perhaps been the most devastating attack on a cryptosystem.Conventional public key cryptosystems can revoke public keys in the case of key-exposure. However, the publickey for an attribute-based scheme represents an attribute set should not be changed. Key-Insulation is a crucialtechnique for protecting private keys. To deal with the key-exposure problems in an attribute-based cryptosystem,this paper extends the parallel key-insulated mechanism to ciphertext policy attribute-based encryption scenariosand introduces the primitive of ciphertext policy attribute-based parallel key-insulated encryption (CPABPKIE).After formalizing the definition and security notions for CPABPKIE, a concrete CPABPKIE scheme is presented.The security the proposed CPABPKIE scheme can be proved in the selective-ID model. The new primitive does notincrease the risk of helper key-exposure, and allows frequent key updating.