The evolution of duplicate genes has been a topic of broad interest. Here, we propose that the conservation of gene family size is a good indicator of the rate of sequence evolution and some other biological properties. By comparing the human-chimpanzee-macaque orthologous gene families with and without family size conservation, we demonstrate that genes with family size conservation evolve more slowly than those without family size conservation. Our results further demonstrate that both family expansion and contraction events may accelerate gene evolution, resulting in elevated evolutionary rates in the genes without family size conservation. In addition, we show that the duplicate genes with family size conservation evolve significantly more slowly than those without family size conservation. Interestingly, the median evolutionary rate of singletons falls in between those of the above two types of duplicate gene families. Our results thus suggest that the controversy on whether duplicate genes evolve more slowly than singletons can be resolved when family size conservation is taken into consideration. Furthermore, we also observe that duplicate genes with family size conservation have the highest level of gene expression/expression breadth, the highest proportion of essential genes, and the lowest gene compactness, followed by singletons and then by duplicate genes without family size conservation. Such a trend accords well with our observations of evolutionary rates. Our results thus point to the importance of family size conservation in the evolution of duplicate genes.