In this paper, responses of a new dual-induction resistivity logging-while-drilling (LWD) tool in 3D inhomogeneous formation models are simulated by the vector finite element method (VFEM), the influences of the borehole, invaded zone, surrounding strata, and tool eccentricity are analyzed, and calibration loop parameters and calibration coefficients of the LWD tool are discussed. The results show that the tool has a greater depth of investigation than that of the existing electromagnetic propagation LWD tools and is more sensitive to azimuthal conductivity. Both deep and medium induction responses have linear relationships with the formation conductivity, considering optimal calibration loop parameters and calibration coefficients. Due to the different depths of investigation and resolution, deep induction and medium induction are affected differently by the formation model parameters, thereby having different correction factors. The simulation results can provide theoretical references for the research and interpretation of the dual-induction resistivity LWD tools.