In recent years, the construction of drug carriers that integrate diagnosis and treatment has become a new trend. In this article, a metal–organic framework (Zr-MOF) was synthesized and functionalized using acetaldehyde-modified-cystine (AMC) to form the functional drug carrier Zr-MOF/AMC which could be used to determine the concentration of glutathione (GSH) for cancer diagnosis, and to achieve pH/GSH dual-responsive release of methotrexate (MTX) for cancer therapy. The cleavage of the AMC disulfide bond by GSH generates two fluorescent molecules that produce strongly enhanced fluorescence, and the intensity is proportional to the GSH concentration. The green fluorescence of Zr-MOF/AMC in cancer cells proves that it can be applied in cell imaging to detect abnormal GSH concentrations for early diagnosis. In addition, MTX loaded on the Zr-MOF/AMC is released by the cleavage of the –S–S– and –CN– bonds at the high GSH concentration and low pH in cancer cells. This dual-responsive drug release helps to deliver drugs to cancer cells more precisely. All the experiments suggest that this novel type of pH/GSH dual-responsive Zr-MOF/AMC nanoparticle may serve as a new drug delivery system for cancer diagnosis and treatment.