In this study, we investigated low-frequency and rare variants associated with blood pressure (BP) by focusing on a linkage region on chromosome 16p13. We used whole genome sequencing (WGS) data obtained through the NHLBI Trans-Omics for Precision Medicine (TOPMed) program on 395 Cleveland Family Study (CFS) European Americans (CFS-EA). By analyzing functional coding variants and non-coding rare variants with CADD score > 10 residing within the chromosomal region in families with linkage evidence, we observed 25 genes with nominal statistical evidence (burden or SKAT p < 0.05). One of the genes is RBFOX1, an evolutionarily conserved RNA-binding protein that regulates tissue-specific alternative splicing that we previously reported to be associated with BP using exome array data in CFS. After follow-up analysis of the 25 genes in ten independent TOPMed studies with individuals of European, African, and East Asian ancestry, and Hispanics (N = 29,988), we identified variants in SLX4 (p = 2.19 × 10−4) to be significantly associated with BP traits when accounting for multiple testing. We also replicated the associations previously reported for RBFOX1 (p = 0.007). Follow-up analysis with GTEx eQTL data shows SLX4 variants are associated with gene expression in coronary artery, multiple brain tissues, and right atrial appendage of the heart. Our study demonstrates that linkage analysis of family data can provide an efficient approach for detecting rare variants associated with complex traits in WGS data.