Genome-wide association studies (GWASs) have identified >20 genetic loci associated with human intelligence. However, due to correlations between the trait-associated SNPs, only a few of the loci are confirmed to have a true biological effect. In order to distinguish the SNPs that have a causal effect on human intelligence, we must eliminate the noise from the high degree of linkage disequilibrium that persists throughout the genome. In this study, we apply a novel PAINTOR fine-mapping method, which uses a Bayesian approach to determine the SNPs with the highest probability of causality. This technique incorporates the GWAS summary statistics, linkage disequilibrium structure, and functional annotations to compute the posterior probability of causality for all SNPs in the GWAS-associated regions. We found five SNPs (rs6002620, rs41352752, rs6568547, rs138592330, and rs28371699) with a high probability of causality, three of which have posterior probabilities >0.60. The SNP rs6002620 (NDUFA6), which is involved in mitochondrial function, has the highest likelihood of causality. These findings provide important insight into the genetic determinants contributing to human intelligence.