Vital pulp therapy is an important endodontic treatment. Strategies using growth factors and biological molecules are effective in developing pulp capping materials based on wound healing by the dentin-pulp complex. Our group developed biodegradable viscoelastic polymer materials for tissue-engineered medical devices. The polymer contents help overcome the poor fracture toughness of hydroxyapatite (HAp)-facilitated osteogenic differentiation of pulp cells. However, the composition of this novel polymer remained unclear. This study evaluated a novel polymer composite, P(CL-co-DLLA) and HAp, as a direct pulp capping carrier for biological molecules. The biocompatibility of the novel polymer composite was evaluated by determining the cytotoxicity and proliferation of human dental stem cells in vitro. The novel polymer composite with BMP-2, which reportedly induced tertiary dentin, was tested as a direct pulp capping material in a rat model. Cytotoxicity and proliferation assays revealed that the biocompatibility of the novel polymer composite was similar to that of the control. The novel polymer composite with BMP-2-induced tertiary dentin, similar to hydraulic calcium-silicate cement, in the direct pulp capping model. The BMP-2 composite upregulated wound healing-related gene expression compared to the novel polymer composite alone. Therefore, we suggest that novel polymer composites could be effective carriers for pulp capping.