Simulation of solute diffusion through porous media (membrane) was carried out by a random walk procedure. The porous media used were three kinds of two-dimensional square networks of channels with almost the same average pore diameters and porosities, but with different pore size distributions. In the simulation the partition equilibrium of solute between the bulk feed phase and the membrane phase was established, and the apparent permeability in the steady state was evaluated. First, only the steric interaction between the solute and the pore wall was considered. In spite of the similar average pore diameters and porosities of the networks, the apparent permeability and selectivity were dependent on the kinds of networks. The network with more small pores showed the smaller permeability and the higher selectivity. When the diameter of solute which can be actually transported is fairly smaller than the average pore diameter, the network with broad pore distribution and with more small pores is found to be useful for obtaining higher selectivity. Next, the electrostatic and dispersion (van der Waals) interactions between the solute and the pore wall were introduced in this simulation. By such long-range interactions the selectivity increased while the apparent permeability decreased. This result showed that the introduction of the repulsive electrostatic interaction between membrane and solute is one useful method for enhancing the selectivity. The effects of the kinds of networks on transport properties in the presence of long-range interactions were similar to those in the absence of such interactions.