Diatoms are among the most abundant organisms in nature; however, their relationships with single-stranded DNA (ssDNA) viruses have not yet been defined in detail. We report the isolation and characterisation of a virus (CsetDNAV) that lytically infects the bloom-forming diatom Chaetoceros setoensis. The virion is 33 nm in diameter and accumulates in the nucleus of its host. CsetDNAV harbours a covalently closed-circular ssDNA genome comprising 5836 nucleotides and eight different short-complementary fragments (67-145 nucleotides), which have not been reported in other diatom viruses. Phylogenetic analysis based on the putative replicase-related protein showed that CsetDNAV was not included in the monophyly of the recently established genus Bacilladnavirus. This discovery of CsetDNAV, which harbours a genome with a structure that is unique among known viruses that infect diatoms, suggests that other such undiscovered viruses possess diverse genomic architectures.