We present molecular dynamics simulations of dimyristoylphosphatidylcholine (DMPC) lipid bilayers in the presence of dimethyl sulfoxide (DMSO). The MD simulations focus on understanding the effect of 3 mol % DMSO on structural and permeation properties of DMPC bilayers. The potential of mean force (PMF) and the diffusivity profiles along the normal direction to the bilayer were calculated for water and DMSO molecules in systems containing 0 and 3 mol % DMSO. The simulation results indicate that while the presence of DMSO has only a small effect on diffusion coefficients of both water and DMSO molecules, it affects significantly the corresponding transmembrane free energy profiles. Using the free energy profiles and diffusivities for water and DMSO and by employing an inhomogeneous solubility-diffusion model we calculated the permeability coefficients. Our simulations show that the increase of the concentration of DMSO in the solution to 3 mol % leads to a significant increase, by about 3 times, of the permeability of water through a DMPC bilayer; a permeability increase that might explain in part the unusual ability of DMSO, even at relatively low concentrations, to reduce the osmotic pressure imbalance present during cryopreservation protocols.