For the problem of reduced positioning accuracy of inertial navigation at high latitudes due to rapid convergence of the Earth's meridians, an inertial navigation method in Cartesian coordinates system is proposed, which is applicable to high-latitude areas. The method for establishing Cartesian coordinates system under spherical projection is presented, and the relationship between Cartesian coordinates and quasi-Cartesian coordinates is analyzed. The newly established inertial navigation method in Cartesian coordinates system is expounded, with reckoning of the ship's velocity, position and error. A switching model between high-latitude navigation mode and traditional navigation mode is established. Theoretical analysis shows that navigation of the inertial system based on the proposed Cartesian coordinates system can provide accurate information on the position and velocity of ships at high-latitude areas.