We report the first complete genome sequence of the marine diatom-infecting, positive-sense single-stranded RNA (ssRNA) virus, Rhizosolenia setigera RNA virus (RsRNAV). The genome is 8877 nucleotides (nt), polyadenylated, lacking a cap structure, and has two large open reading frames (ORFs): ORF-1 (4818 nt), a polyprotein gene coding for replicases, e.g. RNA helicase, RNA-dependent RNA polymerase (RdRp); and ORF-2 (2883 nt), a polyprotein gene coding for structural proteins. The ORFs are separated by a 323 nt intergenic region (IGR), flanked by a 624 nt 5′-untranslated region (UTR) and a 229 nt 3′-UTR. The deduced amino acid sequences for ORF-1 and ORF-2 respectively show considerable similarities to the non-structural and structural proteins of a marine raphidophyte-infecting virus HaRNAV (Heterosigma akashiwo RNA virus). Phylogenetic analyses of concatenated amino acid sequences of RNA helicase and RdRp domains supported the monophyly of RsRNAV, HaRNAV and a marine protist-infecting virus SssRNAV (Schizochytrium single-stranded RNA virus) with moderate bootstrap values of 79–83%, but not at the family level, whilst their monophyly was only weakly supported (50–55%) in the phylogenetic tree based on RdRp whole domain. As a result, comparison of the genome organization and sequence suggests RsRNAV is not a member of any currently defined virus family. In the RdRp tree, the positive-sense ssRNA viruses infecting Stramenopiles (RsRNAV, HaRNAV and SssRNAV) and Alveolata (HcRNAV (Heterocapsa circularisquama RNA virus)) were categorized into phylogenetically distant clades, which suggests a host/virus coevolution. Our study supports the hypothesis that a diverse array of ssRNA viruses exists in marine environments.