This study proposes a new integrated navigation algorithm framework for underwater vehicles, which is based on the Lie group extended Kalman filter (LG-EKF). It can be utilized for initial alignment and inertial navigation system/Doppler velocity log (INS/DVL) integrated navigation. The initial LG-EKF algorithm is improved by replacing the earth-centered earth-fixed frame with the tangent plane frame centered with the starting point and replacing the earth-centered inertial frame with the inertial frame corresponding to the tangent plane frame, which enhances the stability and universality of the filter and makes the parameter settings of the filter simple and intuitive. The new error state’s differential equations are derived. Then the observation equation of in-motion alignment and INS/DVL integrated navigation are established. The experimental results indicate that the convergence speed of the yaw angle errors based on the LG-EKF is significantly faster than that based on the EKF in the scenario of large misalignment angles, and the positioning accuracy of the LG-EKF is higher than that of the EKF in the INS/DVL integrated navigation process after initial alignment.