Drag anchor is one of the most commonly used anchorage foundation types. The prediction of embedded trajectory in the process of drag anchor installation is of great importance to the safety design of mooring system. In this paper, the ultimate anchor holding capacity in the seabed soil is calculated through the established finite element model, and then the embedded motion trajectory is predicted applying the incremental calculation method. Firstly, the drag anchor initial embedded depth and inclination angle are assumed, which are regarded as the start embedded point. Secondly, in each incremental step, the incremental displacement of drag anchor is added along the parallel direction of anchor plate, so the displacement increment of drag anchor in the horizontal and vertical directions can be calculated. Thirdly, the finite element model of anchor is established considering the seabed soil and anchor interaction, and the ultimate drag anchor holding capacity at new position can be obtained. Fourthly, the angle between inverse catenary mooring line and horizontal plane at the attachment point at this increment step can be calculated through the inverse catenary equation. Finally, the incremental step is ended until the angle of drag anchor and seabed soil is zero as the ultimate embedded state condition, thus, the whole embedded trajectory of drag anchor is obtained. Meanwhile, the influences of initial parameter changes on the embedded trajectory are considered. Based on the proposed method, the prediction of drag anchor trajectory and the holding capacity of mooring position system can be provided.