We study how the CoO6 distortion along the c-axis affects the magnetic properties and superconductivity in the novel Co-oxide superconductor NaxCoO2.yH(2)O by analyzing the multiorbital Hubbard model using the fluctuation-exchange approximation. It is shown that through generating the trigonal crystal field, the distortion pushes the Co e'(g) bands up and consequently gives rise to the hole-pocket Fermi surfaces, which have been predicted in the band calculations. As the distortion increases, the hole pockets are enlarged and the ferromagnetic fluctuation as well as the pairing instability increases, which is in good aggreement with recent NQR results. (c) 2006 Elsevier B.V. All rights reserved.