Copper oxide (CuO) nanoparticles were successfully deposited on carbon nanotubes’ (CNTs) surface via complex-precipitation method, the nanocomposite was characterized by transmission electron microscopy (TEM), scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), X-ray powder diffraction (XRD), Raman spectroscopy, Fourier transform infrared (FT-IR) and Brunauer–Emmett–Teller (BET). The catalytic performance of CNTs/CuO on ammonium perchlorate (AP) decomposition was analyzed by differential thermal analyzer (DTA), the DTA results showed its excellent catalytic effect on AP decomposition, as 8 wt.% CNTs/CuO was added in AP, the second exothermic peak temperature decreased by 158 °C. Such composite may be a promising candidate for catalyzing the AP thermal decomposition.