Stress-strain mathematical model of FRP-confined concrete plays an important role in civil engineering, and it should be well understood. Based on first region slope, turning point coordinate and third region slope, the development of stress-strain curve of FRP-confined concrete column is analyzed, and conditions which ideal mathematical model need to meet are point out. A new composite exponent-line model is proposed, which overcomes the weakness of conventional model and is available for both hardening and softening type stress-strain curves. Approaches to determine parameters of the proposed model are presented. Finally, the capability and accuracy of the proposed model in predicting the complete stress-strain process of FRP-confined concrete under axial compression are demonstrated through comparisons between predictions of the proposed model and test results.