This paper investigates the estimation problem of vehicle velocity and propeller angular velocity on the underwater vehicle. Inspired by but different from a high-gain observer, the cascade observer features a cascade structure and adaptive observer gains. In doing so the cascade observer attempts to overcome some of the typical problems that may pose to a high-gain observer. As in the case of a high-gain observer, the cascade observer structure is simple and universal in the sense that it is independent of the system dynamics and parameters. A cascade observer is used for the estimation of velocity from measured position. In the 1st step of the observer, the output is estimated, and the 1st order derivative of measured output is estimated via the 2nd step of the observer. Also, nth order derivative of the output is estimated in the (n+1)th step of the observer. It is shown that the proposed observer guarantees globally asymptotical stability. By simulation results, the proposed observer scheme for the estimations of vehicle velocity and propeller angular velocity shows better performance than the scheme based on the existing observer.