Recent large-scale, genome-wide association studies (GWAS) have identified hundreds of genetic loci associated with general intelligence. The cumulative influence of these loci on brain structure is unknown. We examined if cortical morphology mediates the relationship between GWAS-derived polygenic scores for intelligence (PS_i) and g-factor. Using the effect sizes from one of the largest GWAS meta-analysis on general intelligence to date, PS_i were calculated among 10 P value thresholds. PS_i were assessed for the association with g-factor performance, cortical thickness (CT), and surface area (SA) in two large imaging-genetics samples (IMAGEN N= 1651; IntegraMooDS N= 742). PS_i explained up to 5.1% of the variance of g-factor in IMAGEN (F_1,1640 = 12.2-94.3; P<0.005), and up to 3.0% in IntegraMooDS (F_1,725 = 10.0-21.0; P<0.005). The association between polygenic scores and g-factor was partially mediated by SA and CT in prefrontal, anterior cingulate, insula, and medial temporal cortices in both samples (P_{FWER-corrected} <0.005). The variance explained by mediation was up to 0.75% in IMAGEN and 0.77% in IntegraMooDS. Our results provide evidence that cumulative genetic load influences g-factor via cortical structure. The consistency of our results across samples suggests that cortex morphology could be a novel potential biomarker for neurocognitive dysfunction that is among the most intractable psychiatric symptoms.