Abstract The conventional north-pointing inertial navigation system (INS) always points to the geographic north. However, when the system crosses the pole in the polar region, the geographic north quickly changes with 180 degrees, and the rate of change of the geographic north direction will be infinite. Secondly, when the latitude approaches to 90 degrees, which will lead to singularities in math for the angular velocity caused by vehicle motion. With its special definition and mechanization, the grid coordinate system can solve the above problems. Nevertheless, the error analysis of the grid strapdown INS shows that there are Schuler periodic and Foucault periodic oscillations, which badly degrade the accuracy of the strap-down INS. To address the problem, the external horizontal damping technology is adopted in this paper, wherein the external velocity is provided by the Doppler velocity log (DVL). Finally, the feasibility and the effectiveness of the external damping technology were verified by simulation.