  We propose that spin-triplet pairing mechanism due to disconnected Fermi
surfaces proposed in our previous study [Phys. Rev. B {\bf 63} 174507 (2001)]
may be at work in a recently discovered superconductor Na$_x$CoO$_2$ $\cdot y$
H$_2$O. We introduce a single band effective model that takes into account the
pocket-like Fermi surfaces along with the van Hove singularity near the K point
found in the band calculation results. Applying fluctuation exchange method and
solving the linearized {\'E}liashberg equation, the most dominant pairing is
found to have spin-triplet $f$-wave symmetry, where the nodes of the gap
function do not intersect the pocket Fermi surfaces. Presence of finite $T_c$
is suggested in sharp contrast with cases when the gap nodes intersect the
Fermi surface.
