Stray light is one of the factors exerting negative influences on the image quality of the head-up display based on the geometrical waveguide. Particularly, compared with the architecture used to expand a one-dimensional pupil, the geometrical waveguide expanding the two-dimensional pupil makes it difficult to remove the stray light due to the combined effect from two orthogonal directions. To overcome it, causes of stray light in the two-dimensional geometrical waveguide are analyzed based on the detailed calculation of the parameters that determine the geometry; the corresponding approach is put forward to decrease the percentage of the stray light across the eye box to below 0.1%. The relationship between the resultant combined waveguide and the projection optics is also clarified to obtain the pupil matching. The head-up display integrating the combined waveguide and the designed projection optics achieves the field of 24°×15° and the eye box of 80 mm×80 mm.