Augmented reality (AR) technology has been widely applied across a variety of fields, with head-up displays (HUDs) being one of its prominent uses, offering immersive three-dimensional (3D) experiences and interaction with digital content and the real world. AR-HUDs face challenges such as limited field of view (FOV), small eye-box, bulky form factor, and absence of accommodation cue, often compromising trade-offs between these factors. Recently, optical waveguide based on pupil replication process has attracted increasing attention as an optical element for its compact form factor and exit-pupil expansion. Despite these advantages, current waveguide displays struggle to integrate visual information with real scenes because they do not produce accommodation-capable virtual content. In this paper, we introduce a lensless accommodation-capable holographic system based on a waveguide. Our system aims to expand the eye-box at the optimal viewing distance that provides the maximum FOV. We devised a formalized CGH algorithm based on bold assumption and two constraints and successfully performed numerical observation simulation. In optical experiments, accommodation-capable images with a maximum horizontal FOV of 7.0 degrees were successfully observed within an expanded eye-box of 9.18 mm at an optimal observation distance of 112 mm.