Long intergenic noncoding RNAs (lincRNAs) represent a large portion of the noncoding genes in mammals and other eukaryotes but remains among the least well-understood of genetic factors to date. Here, we systematically analyzed the human SNPs of lincRNAs at a genome level. We found a significantly lower SNP density in lincRNA regions than both their upstream and downstream flanking regions. Functional regions show lower SNP density than other regions in lincRNAs. We revealed that lincRNAs with higher expression levels and broader expression spectrum have significantly lower SNP density. Moreover, we identified lincRNAs that are under recent positive selection and revealed that these lincRNAs show distinct SNP density, expression level, and tissue specificity. Importantly, we identified a genetic variant (rs7990916:T>C) under recent positive selection at a brain-specific lincRNA that significantly affects the structure of normal brain. Analysis of brain magnetic resonance images showed that individuals with CC genotype have significant bigger regional gray matter volume than individuals with TT genotype. Moreover, the genotype of this SNP shows different distribution in normal elders, mild cognitive impairment, and Alzheimer disease subjects, suggesting that this lincRNA may have a role in physiology and pathophysiology of human brain.