At-bit resistivity measurement is a method for geosteering, which could effectively reduce the risk of drilling operations. Simulating the investigation characteristics of an at-bit resistivity logging tool is a means of developing precise tools, but it is difficult to perform this work because of the complex toroidal coil excitation. So a method is needed to simplify it. Based on 3D FEM, the complicated toroidal coils are simplified as an extended voltage dipole and the detection characteristics of the tool are simulated in this paper. The depth of investigation, vertical resolution, the boundary detection capacity and investigation characteristics effect factors of the tool are studied. The simulated results show that depth of investigation relates to the type of mud, the resistivity of the mud and the length of the bottom hole assembly (BHA). The resolution of the tool depends on the BHA length, and the shorter the BHA length is, the higher resolution of the tool is. The tool has the capacity of boundary detection and it has no connection with spacing. The look ahead capacity in conductive formations is better than that of the low-conductivity formations. The shorter the BHA length is, the better boundary detection capacity of the tool is. The results of this paper could provide theoretical support for design and interpretation of at-bit resistivity logging tools.