To resolve the problems of revocation under the quantum computing, combined with Zhang's scheme, the paper constructs an attributed-based encryption which is revocable from lattice. This scheme updates the key which is associated with un-revocable attributes under the binary tree structure. By using the idea of Shamir's threshold secret sharing scheme, a threshold access policy is realized in this paper. The scheme is selectively secure where the security is reduced to the hardness of learning with error problems in the random oracle model. The analysis shows that the scheme is secure under the quantum attack and supports the flexible threshold access policy.