Abstract Background The tiger shark ( Galeocerdo cuvier ) is a large iconic marine predator inhabiting worldwide tropical and subtropical waters. So far, only mitochondrial markers and microsatellites studies have investigated its worldwide historical demography with inconclusive outcomes. Here, we assessed for the first time the genomic variability of tiger shark based on RAD-seq data for 50 individuals from five sampling sites in the Indo-Pacific (IP) and one in the Atlantic Ocean (AO) to decipher the extent of the species’ global connectivity and its demographic history. Results Clustering algorithms (PCA and NMF), F ST and an approximate Bayesian computation framework revealed the presence of two clusters corresponding to the two oceanic basins. By modelling the two-dimensional site frequency spectrum, we tested alternative isolation/migration scenarios between these two identified populations. We found the highest support for a divergence time between the two ocean basins of ~ 193,000 years before present (B.P) and an ongoing but limited asymmetric migration ~ 176 times larger from the IP to the AO ( Nm ~ 3.9) than vice versa ( Nm ~ 0.02). Conclusions The two oceanic regions are isolated by a strong barrier to dispersal more permeable from the IP to the AO through the Agulhas leakage. We finally emphasized contrasting recent demographic histories for the two regions, with the IP characterized by a recent bottleneck around 2000 years B.P. and the AO by an expansion starting 6000 years B.P. The large differentiation between the two oceanic regions and the absence of population structure within each ocean basin highlight the need for two large management units and call for future conservation programs at the oceanic rather than local scale, particularly in the Indo-Pacific where the population is declining.Background The tiger shark ( Galeocerdo cuvier ) is a large iconic marine predator inhabiting worldwide tropical and subtropical waters. So far, only mitochondrial markers and microsatellites studies have investigated its worldwide historical demography with inconclusive outcomes. Here, we assessed for the first time the genomic variability of tiger shark based on RAD-seq data for 50 individuals from five sampling sites in the Indo-Pacific (IP) and one in the Atlantic Ocean (AO) to decipher the extent of the species’ global connectivity and its demographic history. Results Clustering algorithms (PCA and NMF), F ST and an approximate Bayesian computation framework revealed the presence of two clusters corresponding to the two oceanic basins. By modelling the two-dimensional site frequency spectrum, we tested alternative isolation/migration scenarios between these two identified populations. We found the highest support for a divergence time between the two ocean basins of ~ 193,000 years before present (B.P) and an ongoing but limited asymmetric migration ~ 176 times larger from the IP to the AO ( Nm ~ 3.9) than vice versa ( Nm ~ 0.02). Conclusions The two oceanic regions are isolated by a strong barrier to dispersal more permeable from the IP to the AO through the Agulhas leakage. We finally emphasized contrasting recent demographic histories for the two regions, with the IP characterized by a recent bottleneck around 2000 years B.P. and the AO by an expansion starting 6000 years B.P. The large differentiation between the two oceanic regions and the absence of population structure within each ocean basin highlight the need for two large management units and call for future conservation programs at the oceanic rather than local scale, particularly in the Indo-Pacific where the population is declining.