In this paper, we develop a nonlinear controller to achieve trajectory tracking for a velocity-sensorless vertical take-off and landing (VTOL) aircraft with measurement delays. By applying Pade approximation technique, the original controlled system is approximately transformed into an augmented dimension system without any time delay. After constructing full-order observer, error coordinate transformation, and system decomposition, the tracking problem of the newly transformed system is changed into the stabilization problem of two non-minimum phase subsystems and one minimum phase subsystem. The resulting controller not only forces the VTOL aircraft to asymptotically track the desired trajectories, but also drives the unstable internal dynamics which stands for the non-minimum property of VTOL aircraft to follow the causal ideal internal dynamics (IID) solved via stable system center (SSC) method. Numerical simulation results illustrate the effectiveness of the proposed controller.