In many layer-structured materials, constituent layers are bound through van der Waals (vdW) interactions. However, hydrogen bonding is another type of weak interaction which can contribute to the formation of multi-layered materials. In this work, we investigate aluminum hydroxide [Al(OH)3] having hydrogen bonding as an interlayer binding mechanism. We study the crystal structures and electronic band structures of bulk, single-layer, and multi-layer Al(OH)3 using density functional theory calculations. We find that hydrogen bonds across the constituent layers indeed give rise to interlayer binding stronger than vdW interactions, and a reduction of the band gap occurs for an isolated layer as compared to bulk Al(OH)3 which is attributed to the emergence of surface states. We also consider the alkali-halide intercalation between layers and examine how the intercalated atoms affect the atomic and electronic structures of Al(OH)3.