Primary and secondary schools are places where people cluster together. The school buildings are not only the essential carriers to ensure the life safety of teachers and students during the earthquake but also the important places for emergency refuge after the earthquake. Therefore, the anti-collapse capacity and resilience of the school buildings are of great importance in improving the urban earthquake resistance capacity. This paper focuses on the double-span reinforced concrete (RC) frame, the typical school building structure. Based on the results of structural safety appraisement, the reinforcement design is carried out based on the wrapping angle steel method and the sticking fiber-reinforced polymer method. Then, the finite element model of the structure is established, the earthquake records with different characteristics are selected, and the seismic responses of the structure with and without reinforcement under frequent and rare earthquakes are analyzed. Finally, the anti-collapse capacity and resilience of double-span RC frame structures with and without reinforcement under earthquakes with different characteristics are compared based on the collapse probability and residual drift. The results show that the double-span RC frame structure has good seismic performance, and the drifts of the weak layer decrease by 21.89% and 39.40%, respectively, under frequent and rare earthquakes. The characteristics of long-period and velocity pulse in the near-field earthquake greatly influence the anti-collapse capacity and resilience of the double-span RC frame. Considering the PGA equals 1.0g, the collapse probability under near-field earthquake with pulse and near-field earthquake without pulse are 4.45 times and 2.92 times that of the far-field earthquake, respectively. The relative ratio of residual drifts of the weak layer under rare earthquakes is 3.14 and 1.16, respectively. After reinforcement, the collapse probability and weak layer’s residual drift at 1.0g are reduced by 25.34% and 54.87%, respectively.