User revocation is crucial to the practical application of Identity Based Encryption (IBE). The first Revocable Identity Based Encryption (RIBE) scheme from lattice is given by Chen et al. in ACISP 2012, but its security can only be proved in the selective-ID model. Using the IBE scheme suggested by Agrawal et al. in EUROCPYPT 2010, this paper constructs a lattice-based adaptive-ID secure RIBE scheme, so as to solve a problem left open by Chen et al.. This paper also points out that using the blocking technique given by Singh et al. in SPACE 2012, the public key size can be reduced effectively.