It is generally assumed that human intelligence relies on efficient processing by neurons in our brain. Although grey matter thickness and activity of temporal and frontal cortical areas correlate with IQ scores, no direct evidence exists that links structural and physiological properties of neurons to human intelligence. Here, we find that high IQ scores and large temporal cortical thickness associate with larger, more complex dendrites of human pyramidal neurons. We show in silico that larger dendritic trees enable pyramidal neurons to track activity of synaptic inputs with higher temporal precision, due to fast action potential kinetics. Indeed, we find that human pyramidal neurons of individuals with higher IQ scores sustain fast action potential kinetics during repeated firing. These findings provide the first evidence that human intelligence is associated with neuronal complexity, action potential kinetics and efficient information transfer from inputs to output within cortical neurons.