With the advantages of smaller communication overhead and efficient authentication, the strongly designated verifier aggregate signature has been widely applied in routing protocol in ad-hoc networks since it was proposed in 2005. Although there have been several designated verifier aggregate signature schemes, most of them are not sequential and based on the classic number theory problem, which are no longer secure in the quantum era. So looking for the quantum-immune strongly designated verifier signature schemes with sequential aggregation is much urgent. Among the four quantum-immune public key cryptography, lattice-based cryptography enters a rapid development period in the last ten years and have got many achievements, having the advantages of quantum-immune, computing simply and efficiently, and the worst-case to average-case security guarantees. In this paper, we introduced the concept of strongly designated verifier sequential aggregate signature and proposed a quantum-immune strongly designated verifier sequential aggregate signature, which is proven existentially unforgeable under the small integer solution assumption, and is proven non-transferable and robust under the learning with errors assumption . Moreover, we extended the new scheme to be identity-based strongly designated verifier sequential aggregate signature. Finally, in order to avoid key exposure, an extended forward secure strongly designated verifier sequential aggregate signature is presented later, which is also forward secure、 non-transferable and robust.