Four-arm star-shaped (denoted as ‘S’) polymer adamantane-[poly(lactic-co-glycolic acid)-b-poly(N,N’-diethylaminoethyl methacrylate) poly(ethylene glycol) monomethyl ether]4 (S-PLGA-D-P) and its linear (denoted as ‘L’) counterpart (L-PLGA-D-P) were synthesized, then their self-assembled micelles were further developed to be platforms for anticancer drug delivery. Two types of polymeric micelles exhibited strong pH-responsiveness and good drug loading capacity (21.6% for S-PLGA-D-P and 22.9% for L-PLGA-D-P). Using doxorubicin (DOX) as the model drug, their DOX-loaded micelles displayed well controlled drug release behavior (18.5–19.0% of DOX release at pH 7.4 and 77.6–78.8% of DOX release at pH 5.0 within 80 h), good cytocompatibility against NIH-3T3 cells and effective anticancer efficacy against MCF-7 cells. However, the star-shaped polymeric micelles exhibited preferable stability, which was confirmed by the lower critical micelle concentration (CMC 0.0034 mg/mL) and decrease rate of particle sizes after 7 days incubation (3.5%), compared with the linear polymeric micelle L-PLGA-D-P (CMC 0.0070 mg/mL, decrease rate of particle sizes was 9.6%). Overall, these developed polymeric micelles have promising application as drug delivery system in cancer therapy.