A special superlattice structure in which the thickness of each period increases gradually with small amount is designed. The Raman spectra of acoustic phonons for this structure are calculated numerically using the transfer matrix method. The measured Raman spectrum from a SiGe/Si sample demonstrates the features predicted by the calculation : a strong peak from the localized mode within the first gap, an increase in the line width of the folded peak with the phonon branch index, and an asymmetric lineshape with a tail toward high frequency. A schematic picture is given to help in understanding the observed results. Raman spectra with layer thickness fluctuating randomly are also calculated. The main features are similar to those observed in the superlattices with the thickness varying gradually.