Enhancement of efficiency and luminance of organic light-emitting diodes was investigated by the introduction of a lithium carbonate ($Li_2CO_3$) electron-injection layer. Electron-injection layer is used in organic light-emitting diodes to inject electrons efficiently between a cathode and an organic layer. A device structure of ITO/TPD (40 nm)/$Alq_3$ (60 nm)/$Li_2CO_3$ (x nm)/Al (100 nm) was manufactured by thermal evaporation, where the thickness of $Li_2CO_3$ layer was varied from 0 to 3.3 nm. Current density-luminance-voltage characteristics of the device were measured and analyzed. When the thickness of $Li_2CO_3$ layer is 0.7 nm, the current efficiency and luminance of the device at 8.0 V are improved by a factor of about 18 and 3,000 compared to the ones without the $Li_2CO_3$ layer, respectively. The enhancement of efficiency and luminance of the device with an insertion of $Li_2CO_3$ electron-injection layer is thought to be due to the lowering of an electron barrier height at the interface region between the cathode and the emissive layer. This is judged from an analysis of current density-voltage characteristics with a Fowler-Nordheim tunneling conduction mechanism model. In a study of lifetime of the device that depends on the thickness of $Li_2CO_3$ layer, the optimum thickness of $Li_2CO_3$ layer was obtained to be 1.1 nm. It is thought that an improvement in the lifetime is due to the prevention of moisture and oxygen by $Li_2CO_3$ layer. Thus, from the efficiency and lifetime of the device, we have obtained the optimum thickness of $Li_2CO_3$ layer to be about 1.0 nm.