In the current group signature schemes with backward unlinkability and verifier-local revocation (BU-VLR), the size of the public key is linear with the total number of time intervals, and the size of the revocation list (RL) is linear with the total number of time intervals and revoked members. Therefore, the cost is high not only in memory space but also in revocation token computation and revocation check. This paper proposes a BU-VLR group signature scheme under the DTDH assumption and the q-SDH assumption, which has short public key and RL to reduce the overheads in previous schemes. Moreover, it also has shorter signature length and smaller computation in signing.