Polymeric micelles with core–shell–corona nanoarchitecture were designed for intracellular therapeutic anti-cancer drug carriers. Poly(styrene-b-acrylic acid-b-ethylene glycol) (PS-b-PAA-b-PEG) asymmetric triblock copolymer underwent self-assembly in aqueous solution to form spherical micelles with hydrophobic PS core, anionic PAA shell and hydrophilic PEG corona. The anti-cancer drug (doxorubicin, DOX) was successfully incorporated into the polymeric micelles. The in vitro release experiment confirmed that the release of DOX from the micelles was inhibited at pH 7.4. In contrast, an accelerated release of DOX was observed at mildly acidic conditions such as pH 4.5. The excellent biocompatibility of our PS-b-PAA-b-PEG-based micelles made the synthesized nano-carrier best suited for the delivery of anti-cancer drugs.