The microstructure of as-quenched $Al_{70}Cu_{18}Mg_{12}$ alloy has been investigated in detail using transmission electron microscopy. Al nano-crystals about 5 nm with a high density are distributed in the amorphous matrix, indicating amorphous matrix nano-composite can be synthesized in Al-Cu-Mg alloy. The high density of Al nano-crystals indicates very high nucleation rate and sluggish growth rate during crystallization possibly due to limited diffusion rate of solute atoms of Cu and Mg during solute partitioning. The result of hardness measurement shows that the mechanical properties can be improved by designing a nano-composite structure where nanometer scale crystals are embedded in the amorphous matrix.