The ice coating on the transmission line conductors poses a threat to the safe operation of the power grid. Efficient and accurate ice coating monitoring methods are the foundation of line anti-icing and disaster reduction. This paper uses a LiDAR fixed at the top of the tower as the measuring equipment, based on the real-time acquisition of the partial morphological coordinate data of the conductor, and fits the full-section morphological equation of the conductor through the catenary theory to obtain the coordinate data of each position of the conductor, and uses this data as the input of the finite element algorithm to establish a finite element calculation model of the ice coating mass of the conductor. This paper verifies the conductor shape fitted by the model through collecting the point cloud data of the whole section of the conductor by using the unmanned aerial vehicle (UAV). The research results show that the conductor shape fitted by the finite element numerical model in this paper is consistent with the shape of the whole section of the conductor collected by the UAV, and the calculation results of the finite element model are in accordance with the variation rule of ice coating on the conductor. The structural parameters of the conductor will affect the slope change of the corresponding curve between the maximum sag f and the ice coating mass m of the conductor. In practical applications, the application of the model in this paper needs to consider the influence of factors such as temperature changes and wind vibration, and make corresponding calibrations.