Dynamic searchable symmetric encryption (DSSE) is a useful cryptographic tool in encrypted cloud storage. However, it has been reported that DSSE usually suffers from file-injection attacks and content leak of deleted documents. To mitigate these attacks, forward privacy and backward privacy have been proposed. Nevertheless, the existing forward/backward-private DSSE schemes can only support single keyword queries. To address this problem, in this paper, we propose two DSSE schemes supporting range queries. One is forward-private and supports a large number of documents. The other can achieve backward privacy, while it can only support a limited number of documents. Finally, we also give the security proofs of the proposed DSSE schemes in the random oracle model.