Roll angular motion of the modern aircraft operating in non-linear flight modes with a high angle of attack often demonstrates the limit cycle oscillations, which is commonly known as the wing rock phenomenon. Wing rock dynamics are represented by a substantially non-linear model, with parameters varying over a wide range, depending on the flight conditions (altitude, Mach number, payload mass, etc.) and angle of attack. A perspective approach of the wing rock suppression lies in the adaptation methods. In the present paper an application of the simple adaptive control approach with the Implicit Reference Model (IRM) is proposed and numerically studied. The IRM adaptive controller is applied to ensure smooth tracking the roll angle of the reference (desired) trajectory with the simultaneous wing rock prevention. As compared with the previous authors' work, in the present paper more complex and realistic model is employed, where interdependence between aircraft roll and sideslip motions and the limitations on the aileron deflection angle are explicitly taken into account at the stage of the controller design. To this aim, the modification of the IRM control scheme is suggested and numerically studied. The simulation results obtained demonstrate high efficiency of the proposed method.