Initial alignment and localization are important topics in inertial navigation systems, since misalignment and initial position error wholly propagate into the navigation systems and deteriorate the performance of the systems. This paper presents the error convergence characteristics of the hybrid navigation system for underwater vehicles initial position, which is based on an inertial measurement unit (IMU) accompanying a range sensor. This paper demonstrates the improvement on the navigational performance oj the hybrid system with the range information, especially focused on the convergence of the estimation of underwater vehicles initial position error. Simulations are performed with experimental data obtained from a rotating ann test with a fish model. The convergence speed and condition of the initial error removal for random initial position errors are examined with Monte Carlo simulation. In addition, numerical simulation is conducted with an AUV model in lawn-mowing survey mode to illustrate the error convergence of the hybrid navigation System for initial position error.