The Asian swamp eel (Monopterus albus) is an excellent model species for studying sex change and chromosome evolution. M. albus is also widely reared in East Asia and South-East Asia because of its great nutritional value. The low fecundity of this species (about 300 eggs per fish) greatly hinders fries production and breeding programs. Interestingly, about 3–5% of the eels could remain as females for 3 years and lay more than 3,000 eggs per fish, which are referred to as non-sex-reversal (NSR) females. Here, we presented a new chromosome-level genome assembly of such NSR females using Illumina, HiFi, and Hi-C sequencing technologies. The new assembly (Mal.V2_NSR) is 838.39 Mb in length, and the N50 of the contigs is 49.8 Mb. Compared with the previous assembly obtained using the continuous long-read sequencing technology (Mal.V1_CLR), we found a remarkable increase of continuity in the new assembly Mal.V2_NSR with a 20-times longer contig N50. Chromosomes 2 and 12 were assembled into a single contig, respectively. Meanwhile, two highly contiguous haplotype assemblies were also obtained, with contig N50 being 14.54 and 12.13 Mb, respectively. BUSCO and Merqury analyses indicate completeness and high accuracy of these three assemblies. A comparative genomic analysis revealed substantial structural variations (SVs) between Mal.V2_NSR and Mal.V1_CLR and two phased haplotype assemblies, as well as whole chromosome fusion events when compared with the zig-zag eel. Additionally, our newly obtained assembly provides a genomic view of sex-related genes and a complete landscape of the MHC genes. Therefore, these high-quality genome assemblies would provide great help for future breeding works of the swamp eel, and it is a valuable new reference for genetic and genomic studies of this species.