Waveguide near-eye displays (NEDs) consist of a planar waveguide combiner and a coupling-in projection system. A two-dimensional geometrical waveguide (TDGW) can achieve an ultra-thin, large exit pupil diameter (XPD), wide-angle NED. The design method of a single-layer TDGW is presented and discussed in detail in this paper. A high-precision processing technology that can effectively guarantee the parallelism accuracy is also presented. A miniature coupling-in projection optics is designed with a catadioptric structure and integrated with the waveguide accordingly. Finally, a TDGW with a thickness of 1.75 mm is designed and analyzed. The results show that the stray light over the normal light is less than 0.5%, and the illuminance uniformity is well optimized. The field of view is up to 55°, and the XPD exceeds 12mm×10mm at an eye relief (ERF) of 18 mm. A proof-of-concept prototype was fabricated and demonstrated.