Species A rotaviruses (RVAs) are genetically diverse pathogens. These are the most evolutionarily adaptable organisms, with a multitude of mechanisms for evolutionary change. To date, full-genome classification has been proved to be an excellent tool for studying the evolution of unusual rotavirus strains. As limited data are available from Pune (Maharashtra), western India, the current study was undertaken with the aim of understanding the genetic diversity in three (G1P[6], G9P[4] and G9P[4]) unusual RVA strains circulating in Pune, India during 2013–2015. Full-genome analysis of these strains classified them as G1-P[6]-I1-R1-C1-M1-A1-N1-T1-E1-H1, G9-P[4]-I2-R2-C2-[M1-M2_R]-[A1-A2_R]-N2-T2-E6-H2 and G9-[P4-P6_R]-I1-R1-C1-M1-A1-N1-T1-E1-H1. Sequencing and phylogenetic analysis of the structural and non-structural genes of these unusual RVA strains showed nucleotide/amino acid identities of 82.3–98.5 %/77.3–99.8 % and 86.6–97.6 %/89.6–97.8 % between the strains of the study. Evidence of recombination events was found within the genes encoding VP3, VP4 and NSP1, which showed a combination of genetic information for genogroup 1 [M1/P[6]/A1] and genogroup 2 [M2/P[4]/A2] strains. This study will facilitate future investigations into the molecular pathogenesis of such RVAs as the exchange of whole or partial genetic material between rotaviruses through recombination contributes directly to their diversification, adaptation and evolution.