Novel supramolecular copolymer micelles with stimuli-responsive abilities were successfully prepared through the complementary multiple hydrogen bonds of nucleobases and then applied for rapid intracellular release of drugs. First, both adenine-terminated poly(ε-caprolactone) (PCL-A) and uracil-terminated poly(ethylene glycol) (PEG-U) were synthesized. The supramolecular amphiphilic block copolymers (PCL-A:U-PEG) were formed based on multiple hydrogen bonding interactions between PCL-A and PEG-U. The micelles self-assembled from PCL-A:U-PEG were sufficiently stable in water but prone to fast aggregation in acidic condition due to the dynamic and sensitive nature of noncovalent interactions. The low cytotoxicity of supramolecular copolymer micelles was confirmed by MTT assay against NIH/3T3 normal cells. As a hydrophobic anticancer model drug, doxorubicin (DOX) was encapsulated into these supramolecular copolymer micelles. In vitro release studies demonstrated that the release of DOX from micelles was significantly faster at mildly acid pH of 5.0 compared to physiological pH. MTT assay against HeLa cancer cells showed DOX-loaded micelles had high anticancer efficacy. Hence, these supramolecular copolymer micelles based on the complementary multiple hydrogen bonds of nucleobases are very promising candidates for rapid controlled release of drugs.