A base-isolated structure is a civil engineering structure with a long natural vibration period and is easily influenced by the long period spectrum characteristics of seismic ground motion. Some research results show that, compared with far-field ordinary seismic ground motion, an isolated structure may experience greater deformation under far-field long-period ground motion, and that this will cause structural damage. Therefore, the seismic performance of isolated structures under long-period ground motion is worth studying. In this paper, nine far-field long-period ground motion records were chosen from the Pacific Earthquake Engineering Research Center (PEER) as seismic input, and a lead-rubber bearing (LRB) base-isolated structure, based on the design code, was taken as the object of study. The seismic response of the structure was analyzed and compared under far-field ordinary and far-field long-period ground motion, and the effect of long-period ground motion on isolated structures was studied. The damage distribution law for base-isolated structures under long-period ground motion is discussed by defining the damage status of the concrete and steel in the structure. The research results show that the probability of damage to base-isolated structure under long-period ground motion is far greater than under ordinary ground motion. Furthermore, the damage distribution in isolated structures under long-period ground motion is uneven and is mainly concentrated in the bottom floors of the structure.