Due to the large number of repetitive sequences in complex eukaryotic genomes, fragmented and incompletely assembled genomes lose value as reference sequences, often due to short contigs that cannot be anchored or mispositioned onto chromosomes. Here we report a novel method Highly Efficient Repeat Assembly (HERA), which includes a new concept called a connection graph as well as algorithms for constructing the graph. HERA resolves repeats at high efficiency with single-molecule sequencing data, and enables the assembly of chromosome-scale contigs by further integrating genome maps and Hi-C data. We tested HERA with the genomes of rice R498, maize B73, human HX1 and Tartary buckwheat Pinku1. HERA can correctly assemble most of the tandemly repetitive sequences in rice using single-molecule sequencing data only. Using the same maize and human sequencing data published by Jiao et al. (2017) and Shi et al. (2016), respectively, we dramatically improved on the sequence contiguity compared with the published assemblies, increasing the contig N50 from 1.3 Mb to 61.2 Mb in maize B73 assembly and from 8.3 Mb to 54.4 Mb in human HX1 assembly with HERA. We provided a high-quality maize reference genome with 96.9% of the gaps filled (only 76 gaps left) and several incorrectly positioned sequences fixed compared with the B73 RefGen_v4 assembly. Comparisons between the HERA assembly of HX1 and the human GRCh38 reference genome showed that many gaps in GRCh38 could be filled, and that GRCh38 contained some potential errors that could be fixed. We assembled the Pinku1 genome into 12 scaffolds with a contig N50 size of 27.85 Mb. HERA serves as a new genome assembly/phasing method to generate high quality sequences for complex genomes and as a curation tool to improve the contiguity and completeness of existing reference genomes, including the correction of assembly errors in repetitive regions.