In this study, hyaluronic acid (HA) and curcumin (CCM) are used as functional molecular skeletons to prepare a reticular polymer HA-CCM* via the free radical polymerization reaction. The results showed that HA-CCM* formed nanomicelles through self-assembly in the aqueous medium. These nanomicelles were seen as star-shaped micelles and the particle diameter distribution range of 220–280 nm, which are used to carry doxorubicin (DOX) with a high drug loading and an entrapment efficiency. The experiment of drug release in vitro indicated that HA-CCM* micelles showed significant acid sensitivity. The anticancer activity of DOX-loaded by HA-CCM* micelles (HA-CCM* + DOX) was quantified by MTT assay, indicating that the cytotoxicity of HA-CCM* + DOX to human cervical cancer cell line (HeLa) and human renal cell adenocarcinoma cell line (786-O) was significantly improved and to normal human renal epithelial cell line (293A) was obviously reduced. DOX from HA-CCM* + DOX micelles can enter into the cells and resulted in cell death. The multifunctional HA-CCM* micelles have good prospects in the field of drug delivery. Overall, these results confirmed the potential of these nanomicelles for carrying DOX in the improved cancer chemotherapy.