In the presence of the unmodelled dynamics and external time-varying disturbances, letting an underactuated underwater vehicle track a reference trajectory correctly without knowledge of the vehicle's linear velocity is a challenging problem. This study reports a solution to this problem by proposing a linear velocity observer that is based on available states. Furthermore, a fuzzy observer-based tracking controller is designed, where fuzzy logic systems are resorted to approximate the model uncertainties and disturbances. Theoretical analysis demonstrates that the vehicle can converge to a neighbourhood of the reference smooth trajectory, hence achieving a global state that is uniformly and ultimately bounded. In order to validate the performance of the proposed controller, numerical examples are presented. They show that the linear velocity observer can be used to estimate the actual linear velocity and the underwater vehicle is able to track the reference trajectory closely.