The size effects on Raman red shifts in low-dimensional semiconductor nanocrystals are investigated by considering the size-dependent root-mean-square average amplitude associated with the thermal vibration of atoms. The lower limit of vibrational frequency was obtained by matching the calculation results of Raman red shifts with the experimental data of Si, InP, CdSe, CdS0.65Se0.35, ZnO, CeO2, as well as SnO2 nanocrystals. The results indicate the following: (1) the Raman frequency decreases as the nanocrystal size decreases in both narrow and wide bandgap semiconductors; (2) the influence of crystal size on the Raman frequency of nanoparticles is more pronounced than that of nanowires and thin films; and (3) the Raman red shift is ascribed to the size-induced phonon confinement effect and surface relaxation. This model may provide new insights into the fundamental understanding of the underlying mechanism behind the Raman red shifts.