This paper proposes a Key Policy Attribute-Based Encryption (KP-ABE) scheme supporting user's private key revocation under the direct revocation model, without affecting the public key and any user's private key, so the cost of the revocation is small. Based on the access tree, the construction of our scheme is simpler than the construction proposed by Attrapadung which is based on linear Secret Sharing Schemes(LSSS). Its security can be reduced to the q-Bilinear Diffie-Hellman Exponent (q-BDHE) assumption under the standard model.