We have studied stability in organic light-emitting diode depending on buffer layer and cathode. A transparent electrode of indium-tin-oxide(ITO) was used as an anode. An electron injection energy barrier into organic material is different depending on a work function of cathodes. Theoretically, the energy barriers for the electron injection are 1.2 eV, -0.1 eV, and 0.0 eV for Al, LiAl, and LiF/Al at 300 K, respectively. We considered the cases that holes are injected to organic light-emitting diode. The hole injection energy barrier is about 0.7 eV between ITO and TPD without buffer layer. For hole-injection buffer layers of CuPc and PEDOT:PSS, the hole injection energy barriers are 0.4 eV and 0.5 eV, respectively. When the buffer layer of CuPc and PEDOT:PSS is existed, we observed the effects of hole injection energy barrier, and a reduction of operating-voltage. However, in case of PVK buffer layer, the hole injection energy barrier becomes high(1.0 eV). Even though the operating voltage becomes high, the efficiency is improved. A device structure for optimal lifetime condition is ITO/PEDOT:PSS/TPD/$Alq_3$/LiAl at an initial luminance of $300cd/m^2$.