Assembling a large genome using next generation sequencing reads requires large computer memory and a long execution time. To reduce these requirements, we propose an extension-based assembler, called JR-Assembler, where J and R stand for "jumping" extension and read "remapping." First, it uses the read count to select good quality reads as seeds. Second, it extends each seed by a whole-read extension process, which expedites the extension process and can jump over short repeats. Third, it uses a dynamic back trimming process to avoid extension termination due to sequencing errors. Fourth, it remaps reads to each assembled sequence, and if an assembly error occurs by the presence of a repeat, it breaks the contig at the repeat boundaries. Fifth, it applies a less stringent extension criterion to connect low-coverage regions. Finally, it merges contigs by unused reads. An extensive comparison of JR-Assembler with current assemblers using datasets from small, medium, and large genomes shows that JR-Assembler achieves a better or comparable overall assembly quality and requires lower memory use and less central processing unit time, especially for large genomes. Finally, a simulation study shows that JR-Assembler achieves a superior performance on memory use and central processing unit time than most current assemblers when the read length is 150 bp or longer, indicating that the advantages of JR-Assembler over current assemblers will increase as the read length increases with advances in next generation sequencing technology.