This paper aims to study numerically attenuation of whirl amplitude of a Jeffcott rotor with nonlinear cubic stiffness using hysteretic damping based on Bouc-Wen model. In the present work, a modified Jeffcott rotor with linear viscous damping and cubic stiffness excited by harmonic forcing function owing to mass unbalance is studied. The nonlinear cubic stiffness term appears due to either mid-plane stretching of the shaft or by introducing nonlinear spring at the supports. In view of attenuating the vibrational response further, a nonlinear hysteretic damping term based on widely accepted Bouc-Wen model multiplied with a suitable scale factor is introduced into the system equation. Through appropriate choice of parameters of the model, a wide variety of hysteresis loops are obtained to illustrate the influence of Bouc-Wen parameters over the control of the loop size and smoothness. Following a numerical investigation to highlight the benefits of using Bouc-Wen hysteretic damping, time history and frequency response of the system are presented. A comparison between the responses of the system while using cubic stiffness and hysteretic damping reveals the effectiveness of Bouc-Wen hysteretic damping in reducing whirl amplitude in the subcritical range.