This paper proposed an equivalent input disturbance (EID) based approach to control the vertical down-hole drilling process. To describe a drill string which is typically long with large axial-to-radius ratio, a neutral type model is used to accurately capture dynamics of this type of slender string structure. The axial-torsional coupling effect due to drill bit-rock interaction is also included in the model. A new controller is then designed based on the coupled neutral model and the coupling effect is specifically addressed in the design. To address the uncertainty of the bit-rock interaction, the equivalent input disturbance method is used. A new Lyapunov-Krasovskii functional is proposed for the control design. To this end, a series of numerical simulation results are presented to demonstrate the effectiveness of the proposed control scheme.