It is shown in Large Helical Device experiments that transport modeling based on only fluid description is insufficient to express edge transport phenomena in and around a magnetic island with lower collisionality. Furthermore, in recent tokamak experiments, it is found that the so-called stochastic diffusion theory based on "field line diffusion" overestimates the radial energy transport in collisionless edge plasma affected by resonant magnetic perturbations, though the perturbations induce a chaotic behavior in the field lines. These results imply that conventional modeling of edge transport should be reconsidered for a lower collisionality case. A simulation study of neoclassical transport in magnetic islands and ergodic regions is attempted for understanding the fundamental properties of such collisionless edge plasma. By using a drift kinetic equation solver without the assumption of nested flux surfaces (the KEATS code), it is possible to conduct the investigation. In this paper, we report the simulation study of ion transport in the ergodic region, neglecting the effects of an electric field and neutrals. The simulation results are interpreted through the discussion based on statistical studies.