In recent years, the research on ciphertext-policy attribute-based encryption (CP-ABE) scheme design based on learning with errors (LWE) has been a challenging problem, and many researchers have made a lot of attempts at it. At EUROCRYPT 2021, Datta, Komargodski, and Waters proposed the first provably secure direct CP-ABE construction that supports NC${}^1$ circuit access structures. Improving on their work, we propose a CP-ABE scheme. Technically, we use the new lattice two-stage sampling technique of Lai, Liu, and Wang (EUROCRYPT 2021) in the key generation phase instead of the extended trapdoor sampling technique. In this way, we obtain a CP-ABE scheme, which is at least as secure as the original scheme under the same conditions, and has a shorter ciphertext; we provide an innovative design idea for designing CP-ABE schemes only based on LWE, although this is only a partial theoretical work.