In this paper, we present a study on a navigation and control system including a new navigation algorithm for an unmanned underwater track vehicle (UTV). Generally, in underwater navigation, a Doppler velocity log (DVL) is used to measure the velocity of underwater vehicles. However, the UTV cannot use the DVL since it is operated at the bottom of the seafloor. Therefore, in this study, we developed a hybrid navigation system (HNS) consisting of an inertial measurement unit (IMU), a ring laser gyro (RLG) sensor, and an ultrashort baseline (USBL) sensor for underwater vehicles. The system states of the UTV were estimated using the navigation model and the navigation system composed of the RLG and USBL sensors with an extended Kalman filter (EKF). In the navigation system, the attitude control was designed using the RLG sensor, and the position of the UTV relative to that of the global positioning system (GPS) of the surface ship was estimated using the USBL sensor. A new position and orientation estimation algorithm called the compensating hybrid navigation algorithm (CHNA) was developed using the HNS. The developed CHNA was based on a Kalman filter to more accurately estimate the location of a real underwater trenching vehicle called URI-R using hybrid RLG and USBL sensors by filtering out noises and disturbances. To apply the CHNA to the underwater robotics its rocker (URI-R), we developed a small UTV as a test bed and applied the CHNA to the UTV. Then, we applied the CHNA to the URI-R and verified the superior performance of trajectory tracking through a real underwater test.