The virome of a major white wine grape of cultivar Riesling showing decline and leafroll disease symptoms was analyzed through high-throughput sequencing (HTS) using total RNAs as templates and the Illumina HiSeq 2500 platform. Analysis of HTS data revealed the presence of five viruses and three viroids in the infected vine. These viruses are Grapevine leafroll-associated virus 1 (GLRaV-1) and GLRaV-3 (genus Ampelovirus, family Closteroviridae) and three viruses of the family Betaflexiviridae (namely, Grapevine virus A [GVA], Grapevine virus B, and Grapevine rupestris stem pitting-associated virus [GRSPaV]). We also show that multiple distinct strains of three viruses (GLRaV-3, GVA, and GRSPaV) were present in this diseased grapevine. The complete genomes of two novel and highly divergent isolates of GLRaV-3 were determined using the draft genomes derived from HTS data and two independent rapid amplification of cDNA ends (RACE) strategies to obtain sequences at both the 5' and the 3' termini of the viral genomes. Questionable genome regions of both isolates were also verified through cloning of reverse transcription polymerase chain reaction products and Sanger sequencing. These two isolates are vastly divergent from all other isolates of GLRaV-3 whose genome sequences are available in GenBank. Isolate ON8415A has up to 76% nucleotide sequence identities to other isolates representing existing variant groups. We also revealed high degrees of variation in both length and sequence in the terminal untranslated regions (UTRs) of GLRaV-3 variants. The 5'-UTR of most GLRaV-3 isolates whose complete genomes have been sequenced contain tandem repeats of 65 nucleotides, a highly unusual feature rarely observed in (+)single-stranded RNA viruses. Mechanisms for the biogenesis of these tandem repeats and their function in virus replication and pathogenesis require investigation. Findings of this research add to the genetic diversity, evolutionary biology, and diagnostics of GLRaV-3 that afflicts the global grape wine industry.