Human brain has a complex functional architecture and remains active during resting conditions. Resting-state functional magnetic resonance imaging (rsfMRI) measures brain activity at rest, which is closely linked with cognition and clinical outcomes. The role of genetics in human brain function is largely unknown. Here we utilized rsfMRI of 44,190 multi-ethnic individuals (37,339 in the UK Biobank) to discover the common genetic variants influencing intrinsic brain activity. We identified and validated hundreds of novel genetic loci associated with intrinsic functional signatures (P < 2.8 * 10^{-11}), especially for interactions of the central executive, default mode, and salience networks involved in the triple network model of psychopathology. A number of intrinsic brain activity associated loci had been implicated with brain disorders (e.g., Alzheimer's disease, Parkinson's disease, schizophrenia) and cognition, such as 17q21.31, 19q13.32, and 2p16.1. Genetic correlation analysis suggested the shared genetic influences among intrinsic brain function, brain structure, and brain structural connectivity. We also detected significant genetic correlations with 26 other complex traits, such as education, cognitive performance, ADHD, major depressive disorder, schizophrenia, sleep, and neuroticism. Heritability of intrinsic brain activity was enriched in brain tissues. The reported risk genes of Alzheimer's disease typically had stronger associations with intrinsic brain activity than brain structure, and the associated genes of intrinsic brain activity were enriched in multiple biological pathways related to nervous system and neuropathology (P < 1.8 * 10^{-9}).