After connected to the grid, the tri-axial coaxial high temperature superconducting cable would be affected by the short-circuit fault current and generate massive heat and may be damaged. In this paper, the effects of fault parameters and cable structure parameters on operation stability after high current impact are studied by establishing a calculation model of electrothermal coupling, and the operating and transient response characteristics of tri-axial superconducting cables are obtained. By studying the effect of each phase fault on the temperature distribution, impedance characteristics, loss and recovery characteristics of the cable, the comprehensive influence law of various factors affecting the recovery process of loss is expounded. When a three-phase short circuit occurs, the temperature of the A phase conductor rises the highest and its temperature recovery speed is the fastest. When same short-circuit faults occur in each of the three phases, the temperature of the A phase rises the highest and the temperature of the C phase rises the least. The results can provide a basis for judging the safety of tri-axial superconducting cable and improving its stability.