The high variability of the influenza A virus poses a significant threat to public health, therefore monitoring viral strains and studying their genetic properties are important tasks. One part of this monitoring includes sequencing of influenza A viruses of any subtype and analysis of their whole genomes, which is especially important in cases of interspecies adaptation and reassortment. High-throughput sequencing technologies have significantly extended the capabilities of influenza virus epidemiological surveillance. The preparation stages for next generation sequencing (NGS) of influenza A virus include whole genome amplification using one-step RT-PCR, the results of which vary greatly depending on the sample type and quality, that, in turn, affects the coverage of virus fragments and the sequencing results in general. In this work, we propose to supplement the aforementioned technique of whole genome amplification of influenza A virus with sequential suppression PCRs to obtain an even coverage of viral segments of different lengths, which allows sequencing of samples with lower read coverage without decreasing the sequencing quality.