Employing Chemical Vapor Deposition (CVD), we created and then investigated properties of a novel carbon-nanotube porous-copper composite (porous Cu-CNT composite). Field-Emission Scanning Electron Microscopy (FESEM) and Energy-Dispersive X-ray Spectroscopy (EDX) clearly revealed successful coating of CNTs, with its density increasing proportionally with the deposition time. In addition, Raman spectroscopy confirmed the constitution of the composite, which included oxygen, copper, and a high level of carbon. We also found out that the higher density of CNTs led to a significant improvement in light absorption in the visible spectrum, compared with the uncoated porous copper. This special property, combined with the porosity of the copper sample, as well as the exceptional thermal and optical properties of CNTs, makes the composite a highly promising candidate for photothermal applications