Abstract Background Next-generation sequencing (NGS) offers a unique opportunity for high-throughput genomics and has potential to replace Sanger sequencing in many fields, including de-novo sequencing, re-sequencing, meta-genomics, and characterisation of infectious pathogens, such as viral quasispecies. Although methodologies and software for whole genome assembly and genome variation analysis have been developed and refined for NGS data, reconstructing a viral quasispecies using NGS data remains a challenge. This application would be useful for analysing intra-host evolutionary pathways in relation to immune responses and antiretroviral therapy exposures. Here we introduce a set of formulae for the combinatorial analysis of a quasispecies, given a NGS re-sequencing experiment and an algorithm for quasispecies reconstruction. We require that sequenced fragments are aligned against a reference genome, and that the reference genome is partitioned into a set of sliding windows (amplicons). The reconstruction algorithm is based on combinations of multinomial distributions and is designed to minimise the reconstruction of false variants, called in-silico recombinants. Results The reconstruction algorithm was applied to error-free simulated data and reconstructed a high percentage of true variants, even at a low genetic diversity, where the chance to obtain in-silico recombinants is high. Results on empirical NGS data from patients infected with hepatitis B virus, confirmed its ability to characterise different viral variants from distinct patients. Conclusions The combinatorial analysis provided a description of the difficulty to reconstruct a quasispecies, given a determined amplicon partition and a measure of population diversity. The reconstruction algorithm showed good performance both considering simulated data and real data, even in presence of sequencing errors.