A novel amphiphilic acid/light dual-cleavable diblock copolymer poly(epsilon-caprolactone)-acetal-nitrobenzyl ester-poly(ethylene glycol) (PCL-PEG) was prepared via the ring-opening polymerization of epsilon-caprolactone using 5-propargylether-2-nitrobenzyl alcohol as the initiator and subsequent click coupling reaction with azide-terminated poly(ethylene glycol) containing acetal group. Both light-cleavable o-nitrobenzyl methyl ester (ONB) and acid-labile acetal were used as the linkages in between the hydrophilic and hydrophobic polymer blocks. In aqueous solution, the copolymer self-assembled into the spherical polymeric nanoparticles, which were stable under physiological conditions and retained the anticancer drug doxorubicin (DOX) inside. Triggered by acid or UV irradiation, the DOX release rate was significantly enhanced, due to the correspondent degradation of acetal or ONB linkages under the stimulus. In addition, confocal laser scanning microscopy studies further demonstrated the DOX-loaded nanodrug could be efficiently taken up by HeLa cells and exhibited the enhanced DOX release into the cytoplasm upon UV irradiation. Furthermore, in vitro cytotoxicity study verified UV irradiation could improve the antitumor efficacy of the nanodrug against HeLa cells. Thus, this work provides a new method of the design of dual-responsive biodegradable polymers for drug delivery.