Curved surface sliding isolated structures (CSSIS) is a new technology with wide application potentials. However, in engineering practice, the selection of seismic waves controls the seismic design and risk assessment of the CSSIS. A stochastic ground motion model that reflects specific earthquake characteristics was proposed, and the seismic reliability of the CSSIS was evaluated via Monte Carlo simulation (MCS). A mechanical model of the CSSIS was established, and the key structural parameters were determined via shaking-table tests and theoretical analysis. A random ground motion was generated using a stochastic method. Considering the Ninghe area in Tianjin as an example, the failure probability Pf of the CSSIS subjected to the first excursion criterion was calculated. The results show that earthquake magnitude M and source-to-site distance D significantly influence the seismic reliability of the CSSIS. As D increases, Pf of the superstructure decreases rapidly. Conversely, an increase in the earthquake magnitude M leads to an increase in Pf . The research results will provide an important design reference for the wide spread application of CSSIS.