A series of dual stimuli-responsive poly(l-histidine)n-S-S-polyurethane-S-S-poly(l-histidine)n [p(His)n-SS-PU-SS-p(His)n; n = 25, 35, 50, and 75] triblock copolymers that bear two pH-responsive p(His)n end-blocks and PU middle-blocks tethered by a redox-responsive disulphide linker have been synthesized. The resulting triblock copolymers self-assemble to form micelles, nanodaisies (NDs), of uniform size (∼100 nm) and efficiently encapsulate the anticancer drug doxorubicin (Dox) with a high drug loading content (∼19%). The in vitro release profile shows an enhanced release of Dox in an acidic environment in the presence of 10 mM glutathione. The in vitro cell viability assays performed in various cell lines show that the NDs have no acute or intrinsic toxicity. Confocal microscopy images and flow cytometry results show the pH-responsive cellular uptake of Dox-loaded NDs, accelerated at pH ≤ 5.0. The tumour accumulation and in vivo bio-distribution studies of near-infrared dye (IR-820)-labeled NDs show higher tumour accumulation in CT26 tumour-bearing mice within 72 h. Furthermore, the Dox-loaded NDs effectively inhibit the CT26 tumours, suggesting that they are promising nanocarriers for cancer therapy.