Steel fibre reinforced concrete (SFRC) has been increasingly used in super high-rise buildings, nuclear facilities and infrastructures in recent years. Fire is one of the inevitable threats to these structures during their service life, therefore it is of great significance to study the behaviour of SFRC at elevated temperatures. In this study, a new temperature-dependent constitutive model is proposed to describe the mechanical behaviour of SFRC at elevated temperatures. In the present model, the plastic damageof SFRC is considered using the sum of accumulated shear damage and compaction damage, and a temperature-dependent coefficient is introduced to evaluate the plastic strain at fracture. To predict the mechanical properties of SFRC at elevated temperatures, a set of equations are proposed based on the collected experimental data. Particularly, three indexes, i.e. water to binder ratio, moisture content and alumina content, are introduced to calibrate the normalised compressive strength of SFRC. Besides, the effects of fibre dosage and fibre shape are taken into account. The proposed model is used to predict the mechanical behaviour of SFRC subjected to elevated temperatures and is demonstrated to be effective.