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We present the superconducting (SC) property and high-robustness of structural stability of kagome CsV3Sb5 under in situ high pressures. For the initial SC-I phase, its Tc is quickly enhanced from 3.5 K to 7.6 K and then totally suppressed at P ∼ 10 GPa. With further increasing pressure, an SC-II phase emerges at P ∼ 15 GPa and persists up to 100 GPa. The Tc rapidly increases to the maximal value of 5.2 K at P = 53.6 GPa and slowly decreases to 4.7 K at P = 100 GPa. A two-dome-like variation of Tc in CsV3Sb5 is concluded here. The Raman measurements demonstrate that weakening of E2g mode and strengthening of E1g mode occur without phase transition in the SC-II phase, which is supported by the results of phonon spectra calculations. Electronic structure calculations reveal that exertion of pressure may bridge the gap of topological surface nontrivial states near EF, i.e., disappearance of Z2 invariant. Meanwhile, the Fermi surface enlarges significantly, consistent with the increased carrier density. The findings here suggest that the change of electronic structure and strengthened electron-phonon coupling should be responsible for the pressure-induced reentrant SC. [ABSTRACT FROM AUTHOR]