Regeneration of periodontal tissue remains a challenge. Under periodontitis, osteoclasts are overactivated and bone loss occurs. We incorporated sodium alendronate (Alen), a medication commonly used to treat osteoporosis, into a supramolecular hydrogel system in order to create a novel biomaterial that would promote periodontal bone regeneration by inhibiting osteoclast overactivation. The Nap-Gly-Phe-Phe (NapGFF) peptide chain was modified to synthesize the functional Nap-Alen gelator. Afterward, the Nap-Alen/HAP supramolecular hydrogel composite with a suitable hydroxyapatite (HAP) ratio was constructed, which has outstanding mechanical properties and 3D structure. In addition to its good biocompatibility, it can inhibit the proliferation of bone marrow-derived macrophages (BMDMs) and differentiation of osteoclasts. Due to the simultaneous introduction of porous HAP, the hydrogel with a nanofiber structure was formed into a 3D mesh-like sparse porous composite hydrogel. While enhancing the mechanical properties of the gel, the porous structure facilitated the attachment and migration of bone regeneration-related cells. Therefore, it can effectively promote the regeneration of periodontal bone. In the future, by modifying the biophysical properties and loading stem cells or cytokines, this supramolecular hydrogel composite constructed in this study may provide a new strategy for tissue regeneration engineering and provide a preliminary experimental basis for relevant clinical translational studies.