Current variant discovery approaches often rely on an initial read mapping to the reference sequence. Their effectiveness is limited by the presence of gaps, potential misassemblies, regions of duplicates with a high-sequence similarity and regions of high-sequence divergence in the reference. Also, mapping-based approaches are less sensitive to large INDELs and complex variations and provide little phase information in personal genomes. A few de novo assemblers have been developed to identify variants through direct variant calling from the assembly graph, micro-assembly and whole-genome assembly, but mainly for whole-genome sequencing (WGS) data. We developed SGVar, a de novo assembly workflow for haplotype-based variant discovery from whole-exome sequencing (WES) data. Using simulated human exome data, we compared SGVar with five variation-aware de novo assemblers and with BWA-MEM together with three haplotype- or local de novo assembly-based callers. SGVar outperforms the other assemblers in sensitivity and tolerance of sequencing errors. We recapitulated the findings on whole-genome and exome data from a Utah residents with Northern and Western European ancestry (CEU) trio, showing that SGVar had high sensitivity both in the highly divergent human leukocyte antigen (HLA) region and in non-HLA regions of chromosome 6. In particular, SGVar is robust to sequencing error, k-mer selection, divergence level and coverage depth. Unlike mapping-based approaches, SGVar is capable of resolving long-range phase and identifying large INDELs from WES, more prominently from WGS. We conclude that SGVar represents an ideal platform for WES-based variant discovery in highly divergent regions and across the whole genome.