To investigate dynamic thermal stability of SMES（superconducting magnetic energy storage）magnet，mathematics model of the HTS（high temperature superconductivity）magnet was established based on finite element method(FEM).Simulation of temperature field was carried out when magnet was charged and discharged.The research results showed that when the magnet was excited，the hysterics loss is the main part of power loss，and contributes to temperature rise.The result of simulation shows that the magnet is provided with favorable thermal stability on interrupted load and ensured operating temperature under 30 K by controlling rate and alternation time of excitation current on continuum load.