Due to the incredible property loss and significant fatalities induced by tornadoes each year, tornado research has attracted considerable attention. However, previous studies mainly focused on the wind characteristics of tornadoes with the single-cell flow structure, and only a few targeted tornadoes with the dual-cell flow structure. In addition, the influence of flow structure of the tornado on its wind effects has not been sufficiently explored. This study is therefore aimed to investigate how the number of cells in the flow structure affects the wind effects acting on civil structures through Computational Fluid Dynamics (CFD) simulations. The paper is focused on the single-cell and dual-cell flow structure, both of which belong to the category of single-vortex tornadoes. For completeness, the wind characteristics of both types of tornadoes are also studied and compared. The applied CFD simulation strategies are verified based on a real-world tornado. The obtained results show that, due to the central downdraft in the dual-celled tornado, its turbulence intensity is higher than that of the single-celled tornado. The pressure profile for the dual-celled tornado has a wide, flat distribution, while the corresponding profile for the single-celled tornado has a narrow, single peak. The two drag forces induced by the single-celled tornado follow a typical trend, i.e., they reach their peak values when the dome center moves to the tornado core radius, while the corresponding variations under the dual-celled tornado tend to be more random. Similar observations can be found from the two overturning moments. This suggests that the wind loading induced by the dual-celled tornado is more dynamic than that induced by the single-celled tornado.