The primary aim of this study was to examine the effects of family demographics, family demands, and family appraisal on adaptation in Taiwanese families of children with Down syndrome. A second aim was to assess the potential mediating effect of family appraisal on the relationship between family demands and adaptation. Eighty-three families completed mailed questionnaires. Data were analyzed using a principal component analysis and a mixed linear modeling. Gender, family demands, and family appraisal were significantly associated with individual health. Age of the child with Down syndrome, family demands, and family appraisal significantly accounted for family functioning. Family appraisal partially mediated the relationship between family demands and individual and family adaptation. Identification of family factors that influence adaptation will help in the development of culturally sensitive interventions to improve outcomes in Taiwanese families of children with Down syndrome.