The accumulation of nanotechnology-based drugs has been realized in various ways. However, the concentration of drugs encapsulated by nanomaterials is not equal to the concentration of effective drugs; often, the drugs become effective only when they are released from the nanomaterials as free drugs. This means only when the drugs are rapidly released after the accumulated drug-encapsulating nanomaterials can they truly achieve the purpose of increasing the concentration of drugs in the tumor. Therefore, we herein report a dual-response nano-carrier of glutathione and acid to achieve the rapid release of encapsulated drug and increase the effective drug concentration in the tumor. The nano-carrier was constructed using a dual-responsive amphiphilic copolymer, composed of polyethylene glycol and hydrophobic acetylated dextran and connected by a disulfide bond. In the tumor microenvironment, disulfide bonds could be biodegraded by glutathione that is overexpressed in the tumor, exposing the core of nano-carrier composed of acetylated dextran. Then the acidic environment would induce the deacetylation of acetylated dextran into water-soluble dextran. In this way, the nano-carrier will degrade quickly, realizing the purpose of rapid drug release. The results showed that the drug release rate of dual-responsive nano-carrier was much higher than that of glutathione or acid-responsive nano-carrier alone. Furthermore, both in vitro and in vivo experiments confirmed that dual-responsive nano-carrier possessed more efficient anti-tumor effects. Therefore, we believe that dual-responsive nano-carriers have better clinical application prospects.