The concept of inertial system in general theory of relativity is introduced to inertial navigation using post-Newtonian theory of gravity, and a new model of inertial navigation of spacecraft is proposed. It utilizes the geodesic motion objects around the Earth as the follow-up inertial frame of reference. The special force and gravity gradient measured by accelerometers in spacecraft are employed as the observable, and navigation can be realized by solving the status of the spacecraft relative to the follow-up inertial frame. The method used for high orbit satellite can obtain high measurement accuracy, and its errors mainly come from the measurement accuracy of inertial components as well as the design of geodesic trajectory. There is no error accumulated over time which has existed in current inertial navigation model.