The dynamic equations of an autonomous underwater vehicle (AUV) are described as a nonlinear system with multiple hydrodynamic coefficients which strongly affect the performance, maneuverability and controllability of AUV. On the other hand, the values of these coefficients depend on the vehicle speed and the geometric properties. In this paper, the nonlinear model identification problem of NPS AUV II, as a six degree-of-freedom (DOF) autonomous underwater vehicle, is addressed by using the nonlinear continuous-time extended Kalman filter (EKF) observer with guaranteed convergence. To this end, the hydrodynamic coefficients of AUV are considered as the augmented state variables of a six DOF nonlinear model. Based on the input-output data at the presence of the measurement noise of sensors, the state variables and the hydrodynamic coefficients of the nonlinear model in a (path) helical maneuver, are suitably estimated by using the EKF observer. In order to analyze the numerical performance of the proposed method, the dynamic equations of the vehicle are introduced, and a comparison is made between the identified model outputs and those of the real model.