Ternary Z-scheme photocatalysts were constructed using metal-organic frameworks-based AgI/Ag/Cu$_3$(BTC)$_2$ composites via a facile procedure. The morphology, structure, chemical composition, optical and photo-electrochemical properties of the photocatalysts were analyzed by scanning electron microscopy (SEM), X-ray diffraction(XRD), X-ray photoelectron spectroscopy (XPS) and UV–vis diffuse reflectance (DRS) spectroscopy. The photocatalytic tetracycline (TC) degradation demonstrated that all the AgI/Ag/Cu$_3$(BTC)$_2$ photocatalysts have higher photocatalytic activity than that of pure Cu$_3$(BTC)$_2$ and 20% AgI/Ag/Cu$_3$(BTC)$_2$ has the highest TC degradation efficiency. Moreover,20% AgI/Ag/Cu$_3$(BTC)$_2$ also has greatly enhanced photocatalytic activities with TC degradation rate 3.41 times and 4.42times higher than that of AgI/Cu-BTC and Cu-BTC, respectively. A possible indirect Z-scheme mechanism was alsoproposed according to the trapping experiment and band structures of the photocatalyst. The improved photocatalytic activity of the composite can be attributed to the incorporation of Ag and its Z-scheme structures.