Fiber reinforced polymer (FRP) has been widely used in repairing and strengthening of damaged concrete columns due to its excellent material properties. Most of the existing compressive strength models for FRP-confined concrete columns have been established through regression analyses of experimental data, and only a few models were established based on theoretical derivation. Therefore, to extend these compressive strength models based on theoretical derivation, a new strength model based on the Drucker-Prager yield criterion was established in this article, which is suitable for predicting the strength of FRP-confined circular and square concrete columns with loaddamaged, fire-damaged and strain rate. To study the strength model of FRPconfined concrete columns, the author collected 675 test data from published literature and built a large database containing cross-section type, damage type, damage degree and strain rate. In this database, most of the existing strength models in the published literature and the model proposed in this article were evaluated. The evaluation results show that the model can accurately predict the compressive strength of FRP-confined circular and square concrete columns with undamaged, load-damaged, fire-damaged and strain rate.