Curcumin (CUR) has a bright future in the treatment of cancer as a natural active ingredient with great potential. However, curcumin has a low solubility, which limits its clinical application. In this study, IRMOF-10 was created by the direct addition of triethylamine, CUR was loaded into IRMOF-10 using the solvent adsorption method, and the two were characterized using a scanning electron microscope (SEM), X-ray diffraction (XRD), dynamic light scattering (DLS), Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TG) methods, and Brunauer–Emmett–Teller (BET) analysis. We also used the MTT method, 4′,6-diamidino-2-phenylindole (DAPI) staining, the annexin V/PI method, cellular uptake, reactive oxygen species (ROS), and the mitochondrial membrane potential (MMP) to perform a safety analysis and anticancer activity study of IRMOF-10 and CUR@IRMOF-10 on HepG2 cells. Our results showed that CUR@IRMOF-10 had a CUR load of 63.96%, with an obvious slow-release phenomenon. The CUR levels released under different conditions at 60 h were 33.58% (pH 7.4) and 31.86% (pH 5.5). Cell experiments proved that IRMOF-10 was biologically safe and could promote curcumin entering the nucleus, causing a series of reactions, such as an increase in reactive oxygen species and a decrease in the mitochondrial membrane potential, thereby leading to cell apoptosis. In summary, IRMOF-10 is an excellent drug carrier and CUR@IRMOF-10 is an effective anti-liver cancer sustained-release preparation.