Based on a model for the size-dependent bandgap energy of low-dimensional semiconductor compounds, the alloying effect on the bandgap of nanoscale semiconductors is modeled without any adjustable parameter. The model predicts not only a trend of increasing bandgap with decreasing nanocrystal size but also Vegard's relationship between the bandgap and the alloy composition when the size drops close to twice that of the critical size for the nanocrystals. The model predictions agree with available experimental results for bandgap changes of pseudo-binary IIB-VIB chalcogenide semiconductor nanocrystals.