We report the successful molecular-beam epitaxy growth of high quality CdTe/Cd1-xMgxTe quantum wells (x = 0.27-0.52) on GaAs (100) and (111)B substrates. The effectiveness of the two different buffer layers for providing nearly lattice-matched templates were verified by x-ray diffraction and photoluminescence. Optical properties of excitons in the above quantum wells were investigated. It is observed that, for the (100) sample, the exciton displays double peaks, the peak splitting originating from exciton localization on the monolayer fluctuation of the quantum well width. Our experiments indicate that the influence of such fluctuations can be reduced, and interfaces of exceptional perfection can be obtained by growth of the CdTe/CdMgTe quantum well structures on GaAs (111)B-oriented substrates or by a combined growth of conventional molecular-beam epitaxy and migration-enhanced epitaxy on GaAs (100)-oriented substrate. The photoluminescence spectra indicate that significant reduction of the influence of the monolayer fluctuation was indeed accomplished by these procedures.