We elaborate the synthesis and remarkable photocatalytic efficiency of a series of heterojunction nanocomposites with a cauliflower-like architecture composed of copper oxide (CuO) and single-walled carbon nanotubes (SWCNTs). The photocatalysts with such a peculiar design were constructed via facile recrystallization followed by calcination and were symbolized as CuO-SWCNT-1, CuO-SWCNT-2, and CuO-SWCNT-3, representing the components and calcination time in hours. The photocatalytic efficiency of the synthesized nanocomposite samples were investigated by evaluating the decomposition of methylene blue (MB) solution under natural sunlight exposure. All of the as-synthesized photocatalysts were substantially effectual for the photo-deterioration of MB solution. Moreover, CuO-SWCNT-3 revealed the top photocatalytic capability with 96% decomposition of MB solution in 2 h while being exposed to visible light. Pristine CuO nanocrystals and the SWCNTs were employed as controls, whereas the photocatalytic performance of the hetero-composites was significantly better than that of pure CuO as well as SWCNTs. The recyclability of the photocatalysts was also explored, and the results asserted that the samples could be reused for five cycles without being altered notably in photocatalytic performance or morphology.