Turbulence facilitates fast energy/information transfer across scales in physical systems. These qualities are important for brain function, but it is currently unknown if the dynamic intrinsic backbone of the brain also exhibits turbulence. Using large-scale neuroimaging empirical data from 1,003 healthy participants, we demonstrate turbulent-like human brain dynamics. Furthermore, we build a whole-brain model with coupled oscillators to demonstrate that the best fit to the data corresponds to a region of maximally developed turbulent-like dynamics, which also corresponds to maximal sensitivity to the processing of external stimulations (information capability). The model shows the economy of anatomy by following the exponential distance rule of anatomical connections as a cost-of-wiring principle. This establishes a firm link between turbulent-like brain activity and optimal brain function. Overall, our results reveal a way of analyzing and modeling whole-brain dynamics that suggests a turbulent-like dynamic intrinsic backbone facilitating large-scale network communication.