This paper presents a new experimental method for the estimation of hydrodynamic parameters of underwater vehicles, namely the added mass and drag coefficients. The principle is to accurately record the movement of the vehicle in response to a known time-varying actuating force, and find an optimal solution for the parameters that allows simulating a velocity trajectory that fits the recorded trajectory. The optimal solution is obtained using a Numerical Integration Fitting method, which, employing an error minimization algorithm, successively generates velocity trajectories through numerical integration until the parameters converge. This method is applied to determine the hydrodynamic parameters of a torpedo-shaped Autonomous Underwater Vehicle (AUV). The hydrodynamic parameters obtained are compared and found to be close to their theoretical values. In addition, the use of a time-varying force is shown to provide better and more reliable results than the use of a constant or zero external force.