Transposable elements (TEs) can mobilize inside host genomes, potentially creating genetic variability. Long terminal repeat (LTR) retrotransposons (LTR-RTs) are the most prevalent transposable elements in plants species. Here we show that the analysis of an LTR-retrotransposon insertion in rice linked to an agronomic trait revealed a complex structure with two LTR-RTs tandemly repeated and sharing the internal LTR. This structure is flanked by Target Site Duplications (TSDs) suggesting that it may be the result of a single insertion. The analysis of the genomes of 81 rice varieties assembled from long-read sequences showed that this region is highly polymorphic, with some varieties harboring the entire LTR-RT tandem while others contained the insertion of a single LTR-RT. In order to study the prevalence of these structures we designed IDENTAM, a tool for identifying LTR-RT tandems sharing internal LTRs. Running IDENTAM on the Nipponbare rice accession led us to find 35 putative LTR-RT tandem insertions. In most cases the tandems are flanked by the TSDs and show high similarity between LTRs and between the internal regions, supporting the recent insertion of these structures. Our preliminary analysis of other plant genomes suggest that this is a common phenomenon, at least in plant genomes, that has been overlooked until now.