The gas temperature within hypersonic boundary layer flow is so high that the specific heat of gas is no longer a constant but relates to temperature. How variable specific heat influences on boundary layer flow stability is worth researching. The effect of the variable specific heat on the stability of hypersonic boundary layer flows is studied and compared with the case of constant specific heat based on the linear stability theory. It is found that the variable specific heat indeed has some effects on the neutral curves of both the first-mode and the second-mode waves and on the maximum rate of growth also. Therefore, the relationship between specific heat and temperature should be considered in the study of the stability of the boundary layer.