The traditional therapy of cancer has systemic side effects, and many cancers, such as human breast cancer and lung cancer easily metastasize to bones, leading to the formation of secondary tumours. This study was aimed at enhancing the anti-tumour effect of curcumin (CUR) and preventing tumour spread to the bone. A novel multifunctional redox-responsive and CD44 receptor targeting polymer-drug, poly alendronate-hyaluronan-S-S-curcumin copolymer (ALN-oHA-S-S-CUR) based CUR and alendronate (ALN) were synthesized successfully with the disulphide bond linker. The structure of ALN-oHA-S-S-CUR was characterized by H-NMR. The nanomedicine had natural anti-tumour drugs (CUR) as the hydrophobic kernel, and targeting CD44 receptor oligosaccharides of hyaluronan (oHA) and other anti-tumour drugs (ALN) as hydrophilic shell, named ALN-oHA-S-S-CUR conjugates, which could self-assemble into micelle-like nano-spheres in water via a dialysis method with hydrodynamic diameters of 179 ± 23 nm. Interestingly, the cur-loaded ALN-oHA-S-S-CUR micelles were stable in PBS but were capable of releasing the drug under the reducing environment. The rate of drug release was proportional to the GSH concentration. The uptake and cytotoxicity of micelles were higher in MDA-MB-231 cells than in MCF-7 cells because of a higher expression of the CD44 receptor in the former cell line. And compared to the cur-loaded oHA-CUR micelles, the cur-loaded ALN-oHA-S-S-CUR micelles had a good cellular uptake in 2D cancer cell and penetrability in 3D cancer cell spheroids. These results indicated the active targeting redox-sensitive micelles were promising as intracellular drug delivery systems for cancer treatment.