The scaled boundary finite element method (SBFEM) was extended to solve dam-reservoir interaction problems in the time domain and a dynamic stiffness used in the SBFEM of semi-infinite reservoir in the time domain was proposed, which was evaluated by the Bessel function. Based on the dynamic stiffness, transient responses subjected to horizontal ground motions were analyzed through coupling the SBFEM and finite element method (FEM). A dam was modeled by FEM, while the whole fluid in reservoir was modeled by the SBFEM alone or a combination of FEM and SBFEM. Two benchmark examples were considered to check the accuracy of the dynamic stiffness. Results were compared with those from analytical or substructure methods and good agreements were found.