With the rapid development of atom interferometry, atom interferometers have been widely used in inertial navigation, resource exploration, basic physics and other fields. For precise measurement experiments with multi-loop atom interferometer configuration, it is urgent to establish a high precision theoretical model charactering the relationship between target measurement quantities and measurement results. Based on this, we adopt the idea of co-moving reference frame, so as to transfer the gravity, gravity gradient and Earth’s rotation effects to the laser light field interacting with atoms by translating, rotating and stretching the background spacetime. With this method, we not only can simplify the analysis process of the experimental principle, but also give the analytical results of the high-order interference phase of the multi-loop atom interferometercontaining the gravity gradient and Earth’s rotation. This work will lay a certain theoretical foundation for higher-precision experiment, and will also help to clearly guide the implementation of the experiment.