We consider the stabilization of a class of multivariable nonlinear systems, about an equilibrium point at the origin, using variable structure output feedback control. In particular, the system can be transformed into a normal form with no zero dynamics. A robust high-grain observer is used to estimate the state variables while rejecting the effect of disturbance. A globally bounded discontinuous variable structure controller is designed to compensate for modelling error. We show that the controller can stabilize the closed-loop system and does not suffer from the peaking phenomenon that exists in previous designs.