Effectively engineering the lattice thermal conductivity of materials is the key in current thermal science community.Pressure or compressive strain is one of the most worthwhile processes to modify the thermal transport property of materials,due to its robust tunability and flexibility to realize.While it is well documented in literature that the application of hydrostatic pressure normally increases the thermal conductivity of bulk materials,little work has been performed on abnormal pressure dependent thermal conductivity and the governing mechanism has not been fully understood yet.In this paper,taking bulk telluride systems XTe (X =Hg,Cd,Zn) as examples,we show,by combining first-principle calculation and phonon Boltzmann transport equation,that the thermal conductivity presents diverse pressure dependence although they belong to the same group.The thermal conductivity of ZnTe is independent of pressure,while abnormal negative pressure dependence of thermal conductivity is observed in HgTe.As for CdTe,the trend falls in between HgTe and ZnTe and relies largely on the temperature.By comparing the key contributors of the lattice thermal conductivity,we find that the diverse pressure dependence of the lattice thermal conductivity is governed by the competition between the enhancement of group velocity of longitudinal acoustic and optic modes and the reduction of phonon relaxation time of transverse acoustic modes,with both effects being fully quantified by our calculation.Comparison with traditional bulk systems like silicon further underpins the governing mechanism.The correlation between the diverse thermal transport phenomena and the nature of the atomic bonding is also qualitatively established.These findings are expected to deepen our understanding of manipulating phonon transport of bulk materials via simple compressive strain and are also helpful for related applications,such as optimizing thermoelectric performance.