Assembling genomes from single-cell sequencing data is essential for single-cell studies. However, single-cell assemblies are challenging due to (i) the highly non-uniform read coverage and (ii) the elevated levels of sequencing errors and chimeric reads. Although several assemblers for single-cell data have been proposed in recent years, most of them fail to construct correct long contigs. In this study, we present a new framework called EPGA-SC for de novo assembly of single-cell sequencing reads. The EPGA assembler has designed strategies to solve the problems caused by sequencing errors, sequencing biases, and repetitive regions. However, the extremely unbalanced and richer error types prevent EPGA to achieve high performance in single-cell sequencing data. In this study, we designed EPGA-SC based on EPGA. The main innovations of EPGA-SC are as follows: (i) classifying reads to reduce the proportion of false reads; (ii) using multiple sets of high precision paired-end reads generated from the high precision assemblies produced by other assembler such as SPAdes to overcome the impact of sequencing biases and repetitive regions; and (iii) developing novel algorithms for removing chimeric errors and extending contigs. We test EPGA-SC with seven datasets. The experimental results show that EPGA-SC can generate better assemblies than most current tools in most time in term of MAX contig, N50, NG50, NA50, and NGA50.