The behavior of a Gaussian laser beam propagating in a long absorptive plasma column is studied theoretically. The plasma is represented by a complex refractive index which varies quadratically with transverse position. With an absorption loss which is minimum at the axis, the width of the Gaussian beam will converge at large propagational distance to a constant which depends on the plasma characteristics alone. It is found that stable propagation of a Gaussian beam is obtained without requiring that the transverse variation of the real part of the refractive index be favorable to beam trapping.