We investigate random walk of a particle constrained on cells, where cells behave as a lattice gas on a two dimensional square lattice. By Monte Carlo simulation, we obtain the mean first passage time of the particle as a function of the density and temperature of the lattice gas. We find that the transportation of the particle becomes anomalously slow in a certain range of parameters because of the cross over in dynamics between the low and high density regimes; for low densities the dynamics of cells plays the essential role, and for high densities, the dynamics of the particle plays the dominant role.