We investigated the ground state (GS) properties of the single-orbital t-J-V model in a quarter-filling two-dimensional triangular lattice with the slave-boson mean-field approach. We found that the charge ordering (CO) and spin ordering arising from the spin exchange interaction J competes with that from the inter-site Coulomb interaction V. For comparatively large J, the stable GS is insulating with striped CO and antiferromagnetic ordering, avoiding the homogeneous frustrated phase. Accompanying the insulating CO phase, a small insulating gap is opened. Within a reasonable J and V parameter region, our results are consistent with the recent neutron scattering experiments in Na(0.5)CoO(2), which possibly elucidate its CO, magnetic and other GS properties.