A standard model, one of the lattice Boltzmann models for incompressible flow, is broadly applied in mesoscopic fluid with obvious compressible error. To eliminate the compressible effect and the limits in 2D problems, three different models (He-Luo model, Guo’s model, and Zhang’s model) have been proposed and tested by some benchmark questions. However, the numerical accuracy of models adopted in complex geometry and the effect of structural complexity are rarely studied. In this paper, a 2D dimensionless steady flow model is proposed and constructed by fractal geometry with different structural complexity. Poiseuille flow is first simulated to verify the code and shows good agreements with the theoretical solution, supporting further the comparative study on four models to investigate the effect of structural complexity and grid resolution, with reference results obtained by the finite element method (FEM). The work confirms the latter proposed models and effectively reduces compressible error in contrast to the standard model; however, the compressible effect still cannot be ignored in Zhang’s model. The results show that structural error has an approximately negative exponential relationship with grid resolution but an approximately linear relationship with structural complexity. The comparison also demonstrates that the He-Luo model and Guo’s model have a good performance in accuracy and stability, but the convergence rate is lower, while Zhang’s model has an advantage in the convergence rate but the computational stability is poor. The study is significant as it provides guidance and suggestions for adopting LBM to simulate incompressible flow in a complex structure.