Abstract The formability of high strength Al-Zn-Mg-Cu (7000 series) aluminum alloys can be significantly improved at elevated temperatures, which has been paid more attention in recent decades. The formability of high strength aluminum alloys at elevated temperatures is essentially governed by thermal-damage evolution. In this paper, the main purpose is to propose a modified continuum damage model to describe the damage evolution and predict the fracture behavior of AA7075 at elevated temperatures (300–400 °C). Firstly, the thermal-mechanical behavior and forming limit of AA7075 alloy sheet were experimentally investigated using a series of isothermal uniaxial tensile tests and Nakajima tests at different temperatures and strain rates. A set of uniaxial continuum damage constitutive equations (CDCEs) coupling continuum damage mechanics (CDM) with unified viscoplastic theory was proposed to describe the uniaxial tensile behavior of AA7075. Subsequently, the uniaxial equations were extended into a set of multi-axial CDCEs by introducing a multi-axial damage correction formula to predict the TFLD of AA7075. Besides, the forward Euler method was employed to integrate the proposed CDCEs, and the corresponding material constants of CDCEs were further calibrated by the non-dominated sorting genetic algorithmⅡ(NSGA-Ⅱ). The results illustrate that the thermal flow behavior and the TFLD of AA7075 alloy can be predicted successfully by the proposed damage model. Detailed discussions about the effects of corresponding parameters on the computed TFLD indicate the established multi-axial CDCEs are flexible and beneficial to the application potential in numerical simulation of hot sheet metal forming.