Multidrug resistance (MDR) is a major impediment to the success of cancer chemotherapy. The intracellular accumulation of drug and the intracellular release of drug molecules from the carrier could be the most important barriers for nanoscale carriers in overcoming MDR. We demonstrated that the redox-responsive micellar nanodrug carrier assembled from the single disulfide bond-bridged block polymer of poly(ε-caprolactone) and poly(ethyl ethylene phosphate) (PCL-SS-PEEP) achieved more drug accumulation and retention in MDR cancer cells. Such drug carrier rapidly released the incorporated doxorubicin (DOX) in response to the intracellular reductive environment. It therefore significantly enhanced the cytotoxicity of DOX to MDR cancer cells. It was demonstrated that nanoparticular drug carrier with either poly(ethylene glycol) or poly(ethyl ethylene phosphate) (PEEP) shell increased the influx but decreased the efflux of DOX by the multidrug resistant MCF-7/ADR breast cancer cells, in comparison with the direct incubation of MCF-7/ADR cells with DOX, which led to high cellular retention of DOX. Nevertheless, nanoparticles bearing PEEP shell exhibited higher affinity to the cancer cells. The shell detachment of the PCL-SS-PEEP nanoparticles caused by the reduction of intracellular glutathione significantly accelerated the drug release in MCF-7/ADR cells, demonstrated by the flow cytometric analyses, which was beneficial to the entry of DOX into the nuclei of MCF-7/ADR cells. It therefore enhanced the efficiency in overcoming MDR of cancer cells, which renders the redox-responsive nanoparticles promising in cancer therapy.