A modeling data and optimization algorithm driven electrothermal behavior model of gallium nitride high electron mobility transistor (GaN HEMT) is proposed to facilitate the quantitative analysis of problems caused by high speed switching, such as turn-on overvoltage, false turn-on, oscillation and EMI noise. Compared with the traditional behavior models of GaN HEMT, the proposed model can precisely depict the electrothermal characteristics of GaN HEMT in a wide temperature range in both the first and third quadrants by only two compact equations. Meanwhile, the nonlinear parasitic capacitances of GaN HEMT can be accurately modeled by one compact equation. In addition, an optimization algorithm combing the genetic algorithm and Levenberg-Marquardt algorithm is put forward, and a one-step extraction of modeling parameters is realized based on this optimization algorithm and modeling data, which can reduce the modeling time and work load to a certain degree. Results show that the proposed modeling method can precisely model multiple types of GaN HEMT devices manufactured by different companies. Finally, the correctness and effectiveness of the proposed modeling method was verified by the well-matched simulated dynamic waveforms and experimental measurement data.