We investigate the symmetry of the superconducting gap induced by dominant small-q phonon scattering in a triangular lattice. Using the energy band appropriate for Na_xCoO₂·yH₂O and solving the BCS-like gap equation within the weak coupling theory self-consistently, we find that an f-wave pairing state is favored in this system. It is a consequence of the combined effects of the momentum decoupling due to the small-q phonon scattering, the anisotropy of the local density of states (DOS) in the momentum space and the sufficient effective Coulomb repulsion. We propose that this scenario may provide a new picture for the superconductivity in Na_xCoO₂·yH₂O compounds.