Finite elements methods are used to investigate the thermal-electrical characteristics of gallium-nitride (GaN)light-emitting diodes (LEDs) with different transparent conductive layers (TCLs) and buried depths of electrodes,where the transparent conductive layers include indium tin oxide (ITO),graphene (Gr) and the combination of them (ITO/Gr).The optimal material parameters and the precision and accuracy of the simulation model are validated.Moreover,the parameters sensitivity analysis is carried out as well.The results indicate that the LED with the TCL of a 100-nm ITO or 4-layer Gr has a good thermal-electrical performance from the viewpoint of the maximum temperature and the current density deviation of multiple quantum well (MQW),where the maximum temperature occurs at the n-Pad rather than p-Pad.The compound TCL with a 20-nm ITO and 3-layer Gr reaches a thermal-electrical performance better than that of a 100-nm ITO or 4-layer Gr.Moreover,their maximum temperatures decrease about-0.43％ and 1.21％,and the current density uniformities increase up to -6.09％ and 17.41％,respectively.Furthermore,when the electrode buried depth is 0.51 μm,the thermal-electrical performance of the GaN LEDs can be further improved.