Congenital heart defects (CHD) occur in 40% of patients with trisomy 21, while the other 60% have a structurally normal heart. This suggests that the increased dosage of genes on chromosome 21 is a risk factor for abnormal heart development. Interaction of genes on chromosome 21 or their gene products with certain alleles of genes on other chromosomes could contribute to CHD. Here, we identified a pair of monozygotic twins with trisomy 21 but discordant for a ventricular septal defect and epilepsy. Twin-zygosity was confirmed by microsatellite genotyping. We hypothesized that some genetic differences from post-twinning mutations caused the discordant phenotypes. Thus, next generation sequencing (NGS) technologies were applied to sequence both whole genome and exome of their leukocytes. The post-analyses of the sequencing data revealed 21 putative discordant exonic variants between the twins from either genome or exome data. However, of the 15 variants chosen for validation with conventional Sanger sequencing, these candidate variants showed no differences in both twins. The fact that no discordant DNA variants were found suggests that sequence differences of DNA from leukocytes of monozygotic twins might be extremely rare. It also emphasizes the limitation of the current NGS technology in identifying causative genes for discordant phenotypes in monozygotic twins.