Nuclear pore complexes (NPCs) mediate cargo traffic between the nucleus and the cytoplasm of eukaryotic cells. Nuclear transport receptors (NTRs) carry cargos through NPCs by transiently binding to phenylalanine-glycine (FG) repeats on intrinsically disordered polypeptides decorating the NPCs. Major impediments to understand the transport mechanism are the thousands of FG binding sites on each NPC, whose spatial distribution is unknown, and multiple binding sites per NTR, which leads to multivalent interactions. Using single molecule fluorescence microscopy, we show that multiple NTR molecules are required for efficient transport of a large cargo, while a single NTR promotes binding to the NPC but not transport. Particle trajectories and theoretical modelling reveal a crucial role for multivalent NTR interactions with the FG network and indicate a non-uniform FG repeat distribution. A quantitative model is developed wherein the cytoplasmic side of the pore is characterized by a low effective concentration of free FG repeats and a weak FG-NTR affinity, and the centrally located dense permeability barrier is overcome by multivalent interactions, which provide the affinity necessary to permeate the barrier.