This article proposes a novel thickness-accommodating method to design a void-free for flat-foldable origami pattern without self-intersection. Unlike existing methods, it enables uniform thickness distribution without any holes or voids at any location and maximizes the effective area of the unfolded state. The proposed method is applicable not only to 2D folding but also to a generic flat-foldable degree-4-vertex (D4V) pattern. The pattern's thickness-accommodated configuration to avoid self-intersection is determined through kinematic analysis, and a pattern design flow is provided for the generic D4V systematically. Prototypes of the D4V pattern and a more complex Miura-ori-based tessellation model are fabricated to demonstrate the effectiveness of the proposed method. This method can be employed in the design of more complete and diverse foldable structures, such as a foldable space shield with thick materials.