As a result of a high rate of mutations and recombination events, an RNA-virus exists as a heterogeneous “swarm”. The ability of next-generation sequencing to produce massive quantities of genomic data inexpensively has allowed virologists to study the structure of viral populations from an infected host at an unprecedented resolution. However, high similarity and low frequency of the viral variants impose a huge challenge to assembly of individual full-length genomes. The long read length offered by single-molecule sequencing technologies allows each mutant variant to be sequenced in a single pass. However, high error rate limits the ability to reconstruct heterogeneous viral population composed of rare, related mutant variants. In this paper, we present 2SNV, a method able to tolerate the high error-rate of the single-molecule protocol and reconstruct mutant variants. The proposed protocol is able to eliminate sequencing errors and reconstruct closely related viral mutant variants. 2SNV uses linkage between single nucleotide variations to efficiently distinguish them from read errors. To benchmark the sensitivity of 2SNV, we performed a single-molecule sequencing experiment on a sample containing a titrated level of known viral mutant variants. Our method is able to accurately reconstruct clone with frequency of 0.2% and distinguish clones that differed in only two nucleotides distantly located on the genome. 2SNV outperforms existing methods for full-length viral mutant reconstruction. With high sensitivity and accuracy, 2SNV is anticipated to facilitate not only viral quasispecies reconstruction, but also other biological questions that require detection of rare haplotypes such as genetic diversity in cancer cell population, and monitoring B-cell and T-cell receptor repertoire. The open source implementation of 2SNV is freely available for download at http://alan.cs.gsu.edu/NGS/?q=content/2snv