Abstract: Using the information of voltage phase trajectory to analyze the distribution characteristic of out-of-step oscillation center and predict the splitting section in the real time provides the decision-making basis for the power grid dispatchers. Firstly, for a double machine out-of-step model, it is proved that the voltage phase trajectory of each bus along the line is a circle, whose center coordinate and radius are related to the voltage amplitudes of both sides and the position of the bus. Based on the feature of voltage zero-crossing of the out-of-step oscillation center, the analytical equation to decide whether the distribution characteristic of the out-of-step oscillation center is a circle or a straight line is derived. Then an accurate locating method of the out-of-step oscillation center without the equivalent parameter identification is proposed for the ideal two-group swinging. For the out-of-step oscillation in an actual environment, according to the relationship between the voltage phase trajectory and the original point, a predictive indicator of the line where the out-of-step oscillation center is located is constructed, and the indicator has a fixed threshold zero. Finally, a method of predicting the splitting section is proposed, which realizes the real-time prediction based only on the measured data of the transmission line terminal. The proposed methods are validated using the 500kV double machine system, the IEEE-118 system and the HVDC and AC hybrid power grid. The proposed methods have a high engineering application value and advantages of simple calculation, strong adaptability, good effectiveness.