Abstract: The structural uncertainties of base-isolations (i. e., structural stiffness, structural mass, yielding force and post-yielding stiffness of isolation bearing) are represented by a convex model, while structural input uncertainties are described by a stochastic earthquake ground motion model. A new method for calculating fragility curves of a base-isolated structure is presented, considering base pounding and double uncertainties under near-fault earthquake, and the new concept about robust fragility curves is introduced. The calculation results provide some references to how to select the mechanics parameters of isolation bearings and the size of the isolation gap. According to the sensitivity analysis of the maximum base displacement, the upper structural mass and mechanics parameters of isolation bearings (yielding force and post-yielding stiffness of isolation bearing) have a great influence on the base maximum displacement, while the influence of the upper structural stiffness is small. In addition, the paper provides a new way to calculate robust fragility curves of structures when structural uncertainties and earthquake input uncertainties are simultaneously considered.