Solid oxide fuel cell (SOFC) is a promising energy conversion device. However, the severe temperature fluctuations and slow load switching caused by huge thermal inertia during load tracking are urgent issues to be solved. In this paper, a novel SOFC system with thermal energy storage (TES) was proposed and studied. The 1D models of fuel cell stack and TES were established based on electrochemical and thermodynamic laws. The output power switch between full load and half load was explored as an example, and the dynamic response of the proposed system and traditional SOFC was compared, which was achieved by step changes in current. The results indicated that the maximum fluctuations in the inlet gas temperature of traditional SOFC stacks under load step-down and step-up conditions were 169.21 K and 95.24 K, respectively. TES could maintain a constant gas temperature at the entrance of fuel cell stack, thereby avoiding severe temperature fluctuations in the stack. The proposed system would significantly reduce the maximum temperature gradient during load switching and half-load operation. In addition, compared to traditional SOFCs, the dynamic response time of the system with TES had been reduced from thousands of seconds to around 300 s, which meant that the load step-down and step-up processes had been shortened by 93.79 % and 80.52 %, respectively. The response time of load step-down was longer than that of step-up, due to heat generation within the fuel cell stack. The output power of the proposed system during half load operation was 0.21 KW higher than traditional system, which meant an increase of 7.75 % in output power. Finally, the ramp current was adopted to solve the problem of fuel definition in step-up condition, and the response time of the power was 41 s longer than the step current.