De novo assembly of a human genome using nanopore long-read sequences has been reported, but it used more than 150,000 CPU hours and weeks of wall-clock time. To enable rapid human genome assembly, we present Shasta, a de novo long-read assembler, and polishing algorithms named MarginPolish and HELEN. Using a single PromethION nanopore sequencer and our toolkit, we assembled 11 highly contiguous human genomes de novo in 9 d. We achieved roughly 63× coverage, 42-kb read N50 values and 6.5× coverage in reads >100 kb using three flow cells per sample. Shasta produced a complete haploid human genome assembly in under 6 h on a single commercial compute node. MarginPolish and HELEN polished haploid assemblies to more than 99.9% identity (Phred quality score QV = 30) with nanopore reads alone. Addition of proximity-ligation sequencing enabled near chromosome-level scaffolds for all 11 genomes. We compare our assembly performance to existing methods for diploid, haploid and trio-binned human samples and report superior accuracy and speed.