In order to decrease the Schottky barrier height and sheet resistance between graphene(Gr) and the p-GaN layers in GaN-based light-emitting diodes(LEDs), some transparent thin films with good conductivity and large work function are essential to insert into Gr and p-GaN layers. In this work, the ultra-thin films of four metals(silver(Ag), golden(Au), nickel(Ni), platinum(Pt)) are explored to introduce as a bridge layer into Gr and p-GaN, respectively. The effect of a different combination of Gr/metal transparent conductive layers(TCLs) on the electrical, optical, and thermal characteristics of LED was investigated by the finite element methods. It is found that both the TCLs transmittance and the surface temperature of the LED chip reduces with the increase of the metal thickness, and the transmittance decreases to about 80% with the metal thickness increasing to 2 nm. The surface temperature distribution, operation voltage, and optical output power of the LED chips with different metal/Gr combination were calculated and analyzed. Based on the electrical, optical, and thermal performance of LEDs, it is found that 1.5-nm Ag or Ni or Pt, but 1-nm Au combined with 3 layered(L) Gr is the optimal Gr/metal hybrid transparent and current spreading electrode for ultra-violet(UV) or near-UV LEDs. In order to decrease the Schottky barrier height and sheet resistance between graphene (Gr) and the p-GaN layers in GaN-based light-emitting diodes (LEDs), some transparent thin films with good conductivity and large work function are essential to insert into Gr and p-GaN layers. In this work, the ultra-thin films of four metals (silver (Ag), golden (Au), nickel (Ni), platinum (Pt)) are explored to introduce as a bridge layer into Gr The effect of a different combination of Gr / metal transparent conductive layers (TCLs) on the electrical, optical, and thermal characteristics of LEDs was investigated by the finite element methods. It is found that both the TCLs transmittance and the surface temperature of the LED chip reduces with the increase of the metal thickness, and the transmittance decreases to about 80% with the metal thickness increasing to 2 nm. with different meta Based on the electrical, optical, and thermal performance of LEDs, it is found that 1.5-nm Ag or Ni or Pt, but 1-nm Au combined with 3 layered (L) Gr is the optimal Gr / metal hybrid transparent and current spreading electrode for ultra-violet (UV) or near-UV LEDs.