This study investigates Parker instability in an interstellar medium (ISM) near the Galactic plane using three-dimensional magneto-hydrodynamic simulations Parker instability arises from the presence of a magnetic field in a plasma wherein the magnetic buoyant pressure expels the gas and cause the gas to move along the field lines The process is thought to induce the formation of giant molecular clouds in the Galaxy In this study the effects of cosmic-ray (CR) diffusion are examined The ISM at equilibrium is assumed to comprise a plasma fluid and a CR fluid at various temperatures with a uniform magnetic field passing through it in the azimuthal direction of the Galactic disk After a small perturbation the unstable gas aggregates at the footpoint of the magnetic fields and forms dense blobs The growth rate of the instability increases with the strength of the CR diffusion The formation of dense clouds is enhanced by the effect of cosmic rays (CRs) whereas the shape of the clouds depends sensitively on the initial conditions of perturbation (C) 2010 Elsevier B V All rights reserved