We treat each age-specific income-earning member of the family as an income “source,” and use the source-specific Gini decomposition approach as well as the Lorenz comparison approach to study the impact of the changing population age structure on family income inequality. Empirical analysis using Taiwanese data shows that the pattern of Gini coefficients is significantly affected by the above-mentioned age composition factor. The general implication is that for many developing countries which have recently gone through rapid demographic transition, family income inequality indexed may implicitly embody information as to the age-specific composition of family members, which is irrelevant to the general notion of inequality.