CsV3 Sb5 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 CsV3 Sb5 via measurements of resistivity, dc and ac magnetic susceptibility under various pressures up to 6.6 GPa. 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 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 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. The modification of CDW order around Pc1 has been discussed based on the band structure calculations. This work not only demonstrates the potential to raise Tc of the V-based kagome superconductors, but also offers more insights into the rich physics related to the electron correlations in this novel family of topological kagome metals.