Ciphertext-policy attribute-based encryption (CP-ABE) associates ciphertext with access policies. Only when the user's attributes satisfy the ciphertext's policy, they can be capable to decrypt the ciphertext. Expressivity and security are the two directions for the research of CP-ABE. Most of the existing schemes only consider monotonic access structures are selectively secure, resulting in lower expressivity and lower security. Therefore, fully secure CP-ABE schemes with non-monotonic access structure are desired. In the existing fully secure non-monotonic access structure CP-ABE schemes, the attributes that are set is bounded and a one-use constraint is required by these projects on attributes, and efficiency will be lost. In this paper, to overcome the flaw referred to above, we propose a new fully secure non-monotonic access structure CP-ABE. Our proposition enforces no constraints on the scale of the attributes that are set and permits attributes' unrestricted utilization. Furthermore, the scheme's public parameters are composed of a constant number of group elements. We further compare the performance of our scheme with former non-monotonic access structure ABE schemes. It is shown that our scheme has relatively lower computation cost and stronger security.