Designing diffractive waveguides for head-mounted displays requires wide-angle conical diffraction analysis of multiple gratings. In this work, diffractive waveguide design using the relative direction cosine space, which extends the direction cosine space to a relative space involving refractive indices and can describe grating diffraction through various media, is demonstrated. A diffractive waveguide was fabricated with grating periods of 382 and 270 nm, which generated a monochromatic virtual image image in green light (520 nm). The maximum field of view was measured as 39° with 0.5° deviation from the center of view.