A major factor in determining the sag, and consequently the ground clearance of the line, is the measurement the tension of line. The Dynamic Line Rating (DLR) system has been developed and installed on some existing transmission lines, which helps to monitor the on-line sag, predict short-term sag, and give the risk assessment of the line. The tension monitors were installed between dead-end insulators and the dead-end structure. Through the measured tension, the sag in a dead-end span may be calculated with little error. To predict the sags of the transmission line in the near future accurately, this paper proposes the chaos theory to predict such sag serial times. This paper reconstructs the phase space for the sag time series by C-C method. The C-C method is easier to implement, and less demanding computationally. The singular value decomposition chaotic method is presented to predict the chaotic sag time series and the thermal overload risk of a line with a DLR system installed. As tests, the data analysis shows that the proposed method can reflect the varying rule of transmission line sag, and improve the accuracy of sag prediction effectively.