Intelligence is a highly heritable trait and all measures of intelligence are under the influence of a shared set of genetic loci. Identifying the mechanisms linking this genetic diversity to its cognitive outcomes is important for our understanding of the neurobiology of intelligence. Since the genomic sequences harboring these variants must be expressed in specific cells in order to exert their effects, brain-related traits are logical endophenotypes to begin answering this question. Although pleiotropic influences on brain structure and intelligence have already been reported, it is still unclear how these associations relate to specific morphological properties such as cortical thickness and surface area. Here we present a surface-based, high resolution analysis of genetic correlations between cortical morphological properties and measures of intelligence. We used 661 subjects from extended families involved in the GOBS study. Mean age was 40±13, ranging from 18 to 77 and 414 of the subjects were women. Cognitive measurements included Vocabulary, Matrix reasoning and Full-Scale IQ scores measured by the WASI-II test. Imaging data included seven T1-weighted images per subject, acquired consecutively on a Siemens 3T Trio scanner. The images were co-registered and averaged to increase signal-to-noise ratio and reduce motion artifacts, then processed using the CIVET software to measure cortical thickness, surface area and gray matter volume. Polygenic analyses, covarying for age and sex, were performed using variance decomposition methods implemented in the SOLAR software. Results were corrected for multiple comparisons using the FDR method. All participants provided written informed consent and the study was approved by institutional review boards at UTHSCSA, Yale and McGill University. Estimates of heritability were 0.76±0.08 (p=4.3*10^-21) for Full Scale IQ, 0.58±0.10 (p=2.1*10^-11) for Matrix Reasoning t-score and 0.75±0.08 (p=1.1*10^-22) for Vocabulary t-score. Significant heritabilities were also found for all cortical metrics. For gray matter volume and surface area the highest estimates were found in the ventral precuneus, calcarine cortex, superior temporal gyrus and ventral sensorimotor cortex. For cortical thickness, the highest estimates were found in the superior temporal gyrus, dorsal prefrontal cortex, ventral sensorimotor cortex and insula. All cognitive measures were correlated with local gray matter volume, notably in the prefrontal cortex, superior temporal gyrus and insula. This was also true for surface area but not cortical thickness. Significant genetic correlations were found between IQ and gray-matter volume in the dorso-medial prefrontal cortex, insula, right IFG pars orbitalis, parahippocampal and fusiform gyri. Similarly, genetic correlations between matrix reasoning and surface area were found in the dorso-medial prefrontal cortex. We find that the genetic factors influencing intelligence also influence morphological properties of the cortex, notably in prefrontal and temporal areas. We also show that gray matter volume and surface area offer better potential as endophenotypes than cortical thickness. These results provide a more precise identification of the brain areas through which genetic influences on intelligence are mediated, which could help in elucidating the genetic and neurobiological correlates of intelligence.