Strength and ductility are often a paradox in carbon nanotubes (CNTs) reinforced Cu matrix composite, as well as strength and electrical conductivity. Interface and characteristics of CNTs are critical factors in determining the mechanical properties and conductivity of Cu matrix composites. In the present study, a novel tactic by surface and intratube decoration of CNTs is adopted to break the above mentioned dilemmas. By decorating the surface of CNTs with CuO nanoparticles and taking advantage of the good wettability between CuO and Cu matrix, uniform dispersion of CNTs is realized through ball milling. In the final composite, CuO nanoparticles on the surface of CNTs are reduced to Cu. High density interfacial dislocations and interfacial disordered areas are formed between Cu matrix and CNTs, thus forming a strong interfacial bonding. By decorating the inner walls of CNTs with Cu nanoparticles, the interfacial shear stress between Cu matrix and CNTs is improved due to the extrusion effect of Cu nanoparticles on the inner walls. Moreover, the Cu filled inside the tubes can also reduce the intra-tube resistivity of CNTs by increasing their conducting cross-section. Consequently, the Cu matrix composite with simultaneous improvement of strength (272 MPa), ductility (14.3%) and conductivity (93.6% IACS) is achieved in our present study. This tactic provides a new idea to deal with the strength-ductility and strength-conductivity dilemmas in CNTs reinforced metal matrix composites.