Considering a device structure consisting of multi-stacked layers with different refractive indices, we proposed a composite electrode to diminish total internal reflection, thereby improving the out-coupling efficiency of organic light-emitting diodes (OLEDs). The selected transparent conducting oxide materials for the composite electrode were composed of the same main material, gallium-doped zinc oxide (GZO), to avoid lattice mismatch and reduce interfacial strain. Herein, silicon-doped GZO (SGZO) with a relatively low refractive index was used in combination with molybdenum-doped GZO (MGZO) with a high work function to form a multifunctional transparent composite electrode. High transmittance of 94.5% and adequate sheet resistance of 52.3 Ohm/sq were realized through the design of SGZO/MGZO films on a glass substrate. The tested blue phosphorescent OLEDs with SGZO/MGZO composite anode outperformed devices with other selected single-layer electrodes, achieving a high peak efficiency of 29.0% (57.6 cd/A and 47.6 lm/W). These results demonstrate clear advantages of using this composite-electrode concept for realizing high efficiency OLEDs or other flexible optoelectronics.