In this paper, the UDE (uncertainty and disturbance estimator) based robust control is investigated for a class of non-affine nonlinear systems in a normal form. Control system design for non-affine nonlinear systems is one of the most difficult problems due to the lack of mathematical tools. This is also true even for the exact known non-affine systems because of the difficulty in explicitly constructing the control law. It is shown that the proposed UDE-based robust control strategy leads to a stable system. The most important features of the approach are that (i) by adding and subtracting the control term u, the original non-affine form is transformed into a semi-affine form, which not only simplifies the control design procedure, but also avoids the singularity problem of the controller; (ii) the employment of UDE makes the estimation of the lumped uncertain term which is a function of control input, states and disturbances possible, rather than states alone; and (iii) it does not require any knowledge (e.g., bounds) about the uncertainties and disturbances, except the information about the bandwidth, during the design process. The stability of the closed-loop system is established. Effectiveness of the proposed approach is demonstrated through application to the hard disk driver control problem.