the influence of a return current on the diocotron instability of a relativistic hollow electron beam propagating through a background plasma is investigated within the framework of a cold fluid model. The return current density induced in the background plasma is taken to be steadily proportional to the axial electron beam current density. By making use of the linearized fluid-Maxwell equations, a dispersion relation for the eigenfrequencies of the system is derived and used to examine instabilities. It is found that as the fraction of current neutralization increases, lower mode instabilities become dominant while higher mode perturbations are stabilized except the case of very thin beams. It is also observed that for all values of the fraction of current neutralization, increasing of the plasma density gradient or decreasing of the beam thickness is generally destabilizing effect.