Macroscopic cortical networks are important for cognitive function, but it remains challenging to construct anatomically plausible individual structural connectomes from human neuroimaging. We introduce a new technique for cortical network mapping, based on inter-regional similarity of multiple morphometric parameters measured using multimodal MRI. In three cohorts (two human, one macaque), we find that the resulting morphometric similarity networks (MSNs) have a complex topological organisation comprising modules and high-degree hubs. Human MSN modules recapitulate known cortical cytoarchitectonic divisions, and greater inter-regional morphometric similarity was associated with stronger inter-regional co-expression of genes enriched for neuronal terms. Comparing macaque MSNs to tract-tracing data confirmed that morphometric similarity was related to axonal connectivity. Finally, variation in the degree of human MSN nodes accounted for about 40% of between-subject variability in IQ. Morphometric similarity mapping provides a novel, robust and biologically plausible approach to understanding how human cortical networks underpin individual differences in psychological functions.