Current research of designing prosthetic robotic hands mainly focuses on improving their functionality by devising new mechanical structures and actuation systems. Most of existing work relies on a single structure/system (e.g., bone-only or tissue-only) and ignores the fact that the human hand is composed of multiple functional structures (e.g., skin, bones, muscles, and tendons). This may increase the difficulty of the design process and lower the flexibility of the fabricated hand. To tackle this problem, this paper proposes a three-dimensional (3D) printable multi-layer design that models the hand with the layers of skin, tissues, and bones. The proposed design first obtains the 3D surface model of a target hand via 3D scanning, and then generates the 3D bone models from the surface model based on a fast template matching method. To overcome the disadvantage of the rigid bone layer in deformation, the tissue layer is introduced and represented by a concentric tube-based structure, of which the deformability can be explicitly controlled by a parameter. The experimental results show that the proposed design outperforms previous designs remarkably. With the proposed design, prosthetic robotic hands can be produced quickly with low cost and be customizable and deformable.