This paper presents an integrated navigation system for underwater vehicles to improve the performance of a conventional inertial acoustic navigation system by introducing range measurement. The integrated navigation system is based on a strapdown inertial navigation system (SDINS) accompanying range sensor, Doppler velocity log (DVL), magnetic compass, and depth sensor. Two measurement models of the range sensor are derived and augmented to the inertial acoustic navigation system, respectively. A multirate extended Kalman filter (EKF) is adopted to propagate the error covariance with the inertial sensors, where the filter updates the measurement errors and the error covariance and corrects the system states when the external measurements are available. This paper demonstrates the improvement on the robustness and convergence of the integrated navigation system with range aiding (RA). This paper used experimental data obtained from a rotating arm test with a fish model to simulate the navigational performance. Strong points of the navigation system are the elimination of initial position errors and the robustness on the dropout of acoustic signals. The convergence speed and conditions of the initial error removal are examined with Monte Carlo simulation. In addition, numerical simulations are conducted with the six-degrees-of-freedom (6-DOF) equations of motion of an autonomous underwater vehicle (AUV) in a boustrophedon survey mode to illustrate the effectiveness of the integrated navigation system.