Psychiatric disorders are complex clinical conditions with large heterogeneity and overlap in symptoms, genetic liability and brain imaging abnormalities. Building on a dimensional conceptualization of mental health, previous studies have reported genetic overlap between psychiatric disorders and population-level mental health, and between psychiatric disorders and brain functional connectivity. Here, in 30,701 participants aged 45–82 from the UK Biobank we map the genetic associations between self-reported mental health and resting-state fMRI-based measures of brain network function. Multivariate Omnibus Statistical Test revealed 10 genetic loci associated with population-level mental symptoms. Next, conjunctional FDR identified 23 shared genetic variants between these symptom profiles and fMRI-based brain network measures. Functional annotation implicated genes involved in brain structure and function, in particular related to synaptic processes such as axonal growth (e.g. NGFR and RHOA). These findings provide further genetic evidence of an association between brain function and mental health traits in the population.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12888-023-04905-7.