• Based on the elastic catenary model, a novel predictive model for sag and load on overhead transmission lines is proposed in the paper. • The predictive model comprehensively considers the cross-section shrinkage and the elastic deformation after the transmission line is stretched and the temperature effect. • The model takes local deformations on the transmission line as the input parameters to obtain the sag and load on the overhead transmission line. • This paper proposes a novel monitoring method for overhead transmission lines by combining the novel model with fiber Bragg grating (FBG) sensors. Ice accretion on transmission lines (TLs) is one of the major causes of power grid outages in northern regions. Therefore, how to stably and accurately monitor the icing load and sag on overhead TLs is a top priority. Considering the shortcomings of the existing monitoring methods, a mathematical model based on the elastic catenary model is proposed in this paper, which comprehensively considers the cross-section shrinkage and the elastic deformation after the transmission line (TL) is stretched and the temperature effect. The model takes local deformations on the TL line as the input parameters to obtain the sag and load on the overhead TL. In addition, this paper simulates an engineering case by ABAQUS finite element analysis software, and compares the simulation results with the prediction results of this model and the existing model, which proves that the model has higher accuracy. Finally, this paper proposes a novel monitoring method for TLs by combining the developed model with fiber Bragg grating (FBG) sensors. Not only does this monitoring method have higher accuracy, but it can also be used on older TLs that have been completed.