In this paper an observer based on measured and estimated currents and a kinematic model is designed to estimate the velocity and direction angle of an unmanned vehicle (UV). The Lyapunov stability theory is used to establish the stability conditions for the observer. It is shown that the observer will converge in a finite time and the observer gains satisfy the constraints of the stability conditions. The observed velocity and direction angle are used in the closed loop instead of measured ones for sensorless control of the UV. The velocity and direction angle control of the UV are carried out by a well-tuned PI controller. The experimental results show that the proposed observer can be perfectly implemented for sensorless control without using a mechanical sensor, and satisfying results are obtained. In the experiment, command voltages are used rather than measured ones, and therefore only current sensors are needed for the proposed algorithm.