Convex model was used to consider the uncertainty of earthquake in this paper to solve the problem that the selection of different ground motion records will result in great variability in structural seismic performance analysis. Taking the inter-story displacement angle as seismic performance index, non-probabilistic seismic performance of a reinforced concrete frame was assessed under the motivation of rare earthquake by the capability spectrum analysis method. Then the results were compared with probabilistic seismic performance based on the probabilistic random model. By comparison and analysis, it shows that the evaluation of structural seismic performance based on convex model not only reduces the variability, but also is reasonable and applicable to some extent.