To analyze pedigrees with quantitative trait (QT) and sequence data, we developed a rare variant (RV) quantitative nonparametric linkage (QNPL) method, which evaluates sharing of minor alleles. RV-QNPL has greater power than the traditional QNPL that tests for excess sharing of minor and major alleles. RV-QNPL is robust to population substructure and admixture, locus heterogeneity, and inclusion of nonpathogenic variants and can be readily applied outside of coding regions. When QNPL was used to analyze common variants, it often led to loci mapping to large intervals, e.g., >40 Mb. In contrast, when RVs are analyzed, regions are well defined, e.g., a gene. Using simulation studies, we demonstrate that RV-QNPL is substantially more powerful than applying traditional QNPL methods to analyze RVs. RV-QNPL was also applied to analyze age-at-onset (AAO) data for 107 late-onset Alzheimer’s disease (LOAD) pedigrees of Caribbean Hispanic and European ancestry with whole-genome sequence data. When AAO of AD was analyzed regardless of APOE ε4 status, suggestive linkage (LOD = 2.4) was observed with RVs in KNDC1 and nominally significant linkage (p < 0.05) was observed with RVs in LOAD genes ABCA7 and IQCK. When AAO of AD was analyzed for APOE ε4 positive family members, nominally significant linkage was observed with RVs in APOE, while when AAO of AD was analyzed for APOE ε4 negative family members, nominal significance was observed for IQCK and ADAMTS1. RV-QNPL provides a powerful resource to analyze QTs in families to elucidate their genetic etiology.