The synthesis and complete characterization of both norbomene-derived doxorubicin (mono 1) and polyethylene glycol (mono 2) monomers are clearly described, and their copolymerization by ring-opening metathesis polymerization (ROMP) to get the block copolymer (COPY-DOX) is vividly elaborated. The careful design of these conjugates exhibits properties like well-shielded drug moieties and well-defined nanostructures; additionally, they show solubility in both water and biological medium and also have the important tendency of rendering acid-triggered drug release. The drug release profile suggests the importance of having the hydrazone linker that helps to release the drug exactly at the mild acidic conditions resembling the pH of the cancerous cells. It is also observed that the drug release from micelles of COPY-DOX is significantly accelerated at a mildly acidic pH of 5.5-6, compared to the physiological pH of 7.4, suggesting the pH responsive feature of the drug delivery system with hydrazone linkages. Confocal laser scanning microscopy (CLSM) measurements indicate that these COPY-DOX micelles are easily, internalized by living cells, MTT assays against HeLa and 4T cancer cells showing COPY-DOX micelles have a high anticancer efficacy. All of these results demonstrate that these polymeric micelles that self-assembled from COPY-DOX block copolymers have great scope in the world of medicine, and they also symbolize promising carriers for the pH triggered intracellular delivery of hydrophobic anticancer drugs.