The thermal impedance characteristics of insulated gate bipolar transistor (IGBT) modules are critical for the thermal management and design of electronic devices. This paper proposes a fractional-order equivalent thermal impedance model, which is inspired by the correlation between multi-time-scale dissipation characteristics of heat conduction processes and fractional calculus. The fractional-order equivalent thermal impedance model is derived based on the connection between fractional-order calculus and the Foster thermal network model in mathematical operations, with only two parameters to be identified: heat capacity C and fractional order α. Moreover, this paper provides a parameter identification method for the proposed fractional-order equivalent thermal impedance model based on the multi-objective particle swarm optimization (MOPSO) algorithm. In order to validate the effectiveness and superiority of this work, experiments and comparative works are provided in this paper. The results indicate that the fractional-order equivalent thermal impedance model can accurately describe the frequency domain characteristic curves of the thermal impedance of the Foster thermal network model for IGBT modules, with the difference between the amplitude frequency characteristics not exceeding 1 dB and the difference between the phase frequency characteristics not exceeding 1° within the operating frequency range of (1 kHz, 1 MHz).