Dental pulp is essential for the development and long-term preservation of teeth. Dental trauma and caries often lead to pulp inflammation. Vital pulp therapy using dental pulp-capping materials is an approach to preserving the vitality of injured dental pulp. Most pulp-capping materials used in clinics have good biocompatibility to promote mineralization, but their anti-inflammatory effect is weak. Therefore, the failure rate will increase when dental pulp inflammation is severe. The present study developed an amorphous calcium phosphate/poly (L-lactic acid)-poly (lactic-co-glycolic acid) membrane compounded with aspirin (hereafter known as ASP/PLGA-ASP/ACP/PLLA-PLGA). The composite membrane, used as a pulp-capping material, effectively achieved the rapid release of high concentrations of the anti-inflammatory drug aspirin during the early stages as well as the long-term release of low concentrations of aspirin and calcium/phosphorus ions during the later stages, which could repair inflamed dental pulp and promote mineralization. Meanwhile, the composite membrane promoted the proliferation of inflamed dental pulp stem cells, downregulated the expression of inflammatory markers, upregulated the expression of mineralization-related markers, and induced the formation of stronger reparative dentin in the rat pulpitis model. These findings indicate that this material may be suitable for use as a pulp-capping material in clinical applications.