  Within the charge-spin separation fermion-spin theory, the mechanism of
superconductivity in Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O is studied. It is shown
that dressed fermions interact occurring directly through the kinetic energy by
exchanging magnetic excitations. This interaction leads to a net attractive
force between dressed fermions(then the electron Cooper pairs), and their
condensation reveals the superconducting ground state. The optimal
superconducting transition temperature occurs in the electron doping
concentration $\delta\approx 0.29$, and then decreases for both underdoped and
overdoped regimes, in qualitative agreement with the experimental results.
