CsV3Sb5 is a newly discovered Z2 topological kagome metal showing the coexistence of a charge density wave (CDW)-like order at T* = 94 K and superconductivity (SC) at Tc = 2.5 K at ambient pressure. Here we study the interplay between CDW and SC in CsV3Sb5 via measurements of resistivity and magnetic susceptibility under hydrostatic pressures. We find that the CDW transition decreases with pressure and experience a subtle modification at Pc1 = 0.6-0.9 GPa before it vanishes completely at Pc2 = 2 GPa. Correspondingly, Tc(P) displays an unusual M-shaped double dome character with two maxima around Pc1 and Pc2, respectively, leading to a tripled enhancement of Tc to about 8 K at 2 GPa. The obtained temperature-pressure phase diagram resembles those of many unconventional superconductors, illustrating an intimated competition between CDW-like order and SC. The competition is found to be particularly strong for the intermediate pressure range Pc1 <= P <= Pc2 as evidenced by the broad superconducting transition and reduced superconducting volume fraction. This work not only demonstrates the potential to raise the Tc of the V-based kagome superconductors, but also offers more insights into the rich physics related to the electronic correlations in this novel family of topological kagome metals.
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