Chemotherapy is still an important and effective clinical treatment for cancer. However, individual drugs hardly achieve precise controlled release and targeted therapy, thus resulting in unavoidable side effects. Fortunately, the emergence of drug carriers is expected to solve the above problems. In this work, the MOF-on-MOF strategy was adopted to encapsulate DOX into double-layer NH2-MIL-88B to fabricate a core-shell-structured DOX@NH2-MIL-88B-On-NH2-MIL-88B (DMM) and then realize the pH and GSH dual-responsive controlled DOX release. Because of the core-shell structure, the drug-loading capacity of DMM reached 14.4 wt %, which was nearly twice that of DOX@NH2-MIL-88B (DM), and the controlled release performance of DMM was also improved at the same time, greatly improving the kinetics equilibrium time of DOX from 2 h (DM) to 16 h (DMM) at pH 5.0. Moreover, we found that DMM also possessed peroxidase-like catalytic activity under acidic conditions, which could catalyze H2O2 to produce •OH, exhibiting the potential chemodynamical treatment of cancer. Cell experiments showed that DMM had a significant inhibitory effect against 4T1 cancer cells, and the survival rate of 4T1 cells was less than 20% at 100 ppm.