During the interaction between the sea ice and the conical structure, the ice load is affected by the position of the sea ice acting on the conical structure when the tidal water level changes. In this study, the discrete element method (DEM) with the bond and failure model is adopted to simulate the breaking process of sea ice acting on the conical structure. In DEM simulations, the influence of the ice temperature at the top and bottom surface of ice cover on the ice strength is considered. The ice load and the failure mode of ice cover simulated with DEM are compared well with the field data in the Bohai Sea. The DEM results indicate that the bending failure of ice cover occurs when it acts on the upward or downward cone. For both of the upward and downward cone, the ice load increases with the increase of the cone diameter at water level, but the ice load on upward cone is larger than that of downward cone. Meanwhile, the breaking length of ice cover on upward cone is smaller than that on the downward cone. The reasons for the difference of ice load and breaking length between upward cone and downward cone are analyzed based on the DEM results and the filed observation in the Bohai Sea. Moreover, when the sea ice interacts with the interface of upward and downward cone, bending damage generally occurs. When the height of the ice cover center is very close to the height of the upward-downward cone interface, the local ice crushing occurs, but the ice load does not increase significantly. Therefore, the downward conical structure has better performance of ice resistance with effectively reducing the ice load. The DEM can be adopted to understand the mechanism of ice cover failure process, and provide reference for the anti-ice design of structures in cold ocean engineering.