A nanoparticle with a specific response to tumor extracellular acidity provides a new option in the design of tumor-targeted delivery systems. In this study, we report such a pH-responsive polymer which realizes an "off-on" release of bortezomib in tumor acidic microenvironments. A dendrimer surface is grafted with a neutral shell to reduce its cellular uptake, and its interior is functionalized with catechol moieties. An anticancer drug, bortezomib, is loaded within the dendrimer interior via a boronate-catechol interaction. The bortezomib-loaded dendrimer is non-toxic to a number of cells under physiological conditions, but kills most of the cells in slightly acidic microenvironments. In vivo studies further prove that the bortezomib-loaded dendrimer significantly inhibits tumor growth while causing minimal systemic toxicity to the animals. Since there are a number of potent anticancer drugs containing the boronate structure, the polymeric vector in this study provides a versatile scaffold to design pH-responsive drug carriers for chemotherapy.