This work presents a new trajectory tracking control strategy for a three phase Voltage Source Converter (VSC). The design is based on a third order nonlinear model of the VSC expressed in the dq frame. By suitable approximation of the dc voltage dynamics, the system is transformable to a LTI form by a nonlinear change of state coordinates. In these new state coordinates we use a Lyapunov function argument to derive an adaptive control which is robust to parametric uncertainty. This controller can track smooth reference trajectories for q-axis current and dc voltage. A simulation result demonstrates asymptotic reference tracking in the face of parameter error.