Equilibrium and nonequilibrium molecular dynamics simulations are performed to calculate the diffusion coefficient and electric conductivity of ions in a 0.1 M concentration solution confined in neutral cylindrical pores. The applied model is a solvent primitive model (SPM) in which both ions and solvent molecules are soft core spheres and the polar nature of the solvent is represented implicitly as a background with a given dielectric constant. The simulations are carried out in an isokinetic ensemble, and the system, responsing to an applied electric field, is maintained at constant temperature by a Gaussian thermostat. From equilibrium molecular dynamics, diffusion coefficients of ions and solvent decrease with decreasing pore radius or increasing packing fraction of solvent particles. The conductivity determined by nonequilibrium molecular dynamics shows a similar trend, but the pore-size dependence of conductivity does not have a local maximum as was found in the restricted primitive model in which solvent spheres are absent. Using the Nernst-Einstein relation, the ionic conductivity is also calculated from the equilibrium diffusion coefficient and compared with the conductivity obtained from nonequilibrium simulations. The comparison shows that the Nernst-Einsten relation is not valid only at low solvent packing and in very small pores.