  Recently synthesized Kagome compounds AV$_3$Sb$_5$ attract great attention
due to the unusual coexistence of the topology, charge density wave and
superconductivity. In this {\it Letter}, based on the band structures for
CsV$_3$Sb$_5$ in pristine phase, we fit an effective 6-band model for the
low-energy processes; utilizing the random phase approximation (RPA) on the
effective minimal model, we obtain the momentum-resolved static spin
susceptibility attributing the spin-fluctuation pairing mechanism, we find that
the superconducting pairing strengths increase with the lift of the Coulomb
correlation, and the superconductive pairing symmetry is singlet, the gap
functions are antisymmetric with respect to the x-axis and the y-axis in the
intermediate to strong Coulomb correlated regime,indicating the unconventional
superconductivity in Kagome compounds AV$_3$Sb$_5$.
