Structural variants (SVs) account for a large amount of sequence variability across genomes and play an important role in human genomics and precision medicine. Despite intense efforts over the years, the discovery of SVs in individuals remains challenging due to the diploid and highly repetitive structure of the human genome, and by the presence of SVs that vastly exceed sequencing read lengths. However, the recent introduction of low-error long-read sequencing technologies such as PacBio HiFi may finally enable to overcome these barriers. Here we present SVDSS, a novel hybrid method for discovery of SVs from long-read sequencing technologies (e.g., PacBio HiFi) that combines and effectively leverages mapping-free, mapping-based and assembly-based methodologies for overall superior SV discovery performance. Our experiments on several human samples show that SVDSS outperforms state-of-the-art mapping-based methods for discovery of insertion and deletion SVs in PacBio HiFi reads and achieves significant improvements in calling SVs in repetitive regions of the genome. SVDSS is open source and publicly available at https://github.com/Parsoa/SVDSS.