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This work presents the evolution of the electronic properties of kagome superconductor CsV3Sb5 under pressure. The magnetoresistance under high fields of 43 T showed clear Shubnikov–de Haas (SdH) oscillations with multiple frequencies up to 2000 T. With the application of pressure, we observed a sudden change in SdH oscillations with the disappearance of the high-frequency signal near the critical pressure Pc1 ∼ 0.7 GPa. We argue that this change could be due to a reconstruction of the Fermi surface (FS) in CsV3Sb5. To interpret our experimental data, we computed the electronic band structures and FS of CsV3Sb5 using ab initio density functional theory. Our results indicate that both the electronic bands and FS of CsV3Sb5 are highly sensitive to external pressure. The deformation of FS pockets with increasing pressure qualitatively explains our experimental observations. The pressure-driven FS instability in CsV3Sb5 may induce changes in its electronic states, such as superconductivity, charge density wave, nontrivial topology, and more. Therefore, these results are invaluable for gaining insights into these electronic states in CsV3Sb5, as well as in other kagome materials.