In this study, we describe the design, synthesis, and physicochemical and preliminary biological characteristics of new biodegradable, high-molecular-weight (HMW) drug delivery systems with star-like architectures bearing the cytotoxic drug doxorubicin (DOX) attached by a hydrazone bond-containing spacer. The star polymers were synthesized by grafting semitelechelic N-(2-hydroxypropyl) methacrylamide (HPMA) copolymers on a 2,2-bis(hydroxymethyl)propionic acid- (bis-MPA-) based polyester dendritic core. The molecular weight of the star polymers ranged from 280 to 450 000 g/mol and could be adjusted by proper selection of the bis-MPA dendrimer generation and by considering the polymer to dendrimer molar ratio. The biodegradation of the polymer conjugates is based on the spontaneous slow hydrolysis of the dendritic core in neutral physiological conditions. Hydrazone spacers in the conjugates were fairly stable at neutral pH (7.4) mimicking blood stream conditions, and DOX was released from the conjugates under mild acidic conditions simulating the tumor cell microenvironment in endosomes and lysosomes (pH 5). Finally, we have shown the significant in vitro cytotoxicity of the star polymer-DOX conjugate on selected cancer cell lines with IC50 values almost comparable with that of the free drug and higher than that observed for a linear polymer-DOX conjugate with much lower molecular weight.