Haplotype-resolved de novo assembly of highly diverse virus genomes is critical in prevention, control and treatment of viral diseases. Current methods either can handle only relatively accurate short read data, or collapse haplotype-specific variations into consensus sequence. Here, we present Strainline, a novel approach to assemble viral haplotypes from noisy long reads without a reference genome. As a crucial consequence, Strainline is the first approach to provide strain-resolved, full-length de novo assemblies of viral quasispecies from noisy third-generation sequencing data. Benchmarking experiments on both simulated and real datasets of varying complexity and diversity confirm this novelty, by demonstrating the superiority of Strainline in terms of relevant criteria in comparison with the state of the art.