In this work, a novel strategy for improving the interface thermal conductivity (ITC) between the vertically aligned carbon nanotube (VACNT) arrays and copper was proposed and verified using the non-equilibrium molecular dynamics (NEMD) simulations. The introduced metal elements (Ag, Al, Ti, and Ni) enhanced the ITC of the Cu-VACNT interface region via a strong adhesive force. Notably, different from the physisorption between Ag/Al elements and VACNT, a strong interfacial interaction was introduced between the chemically bonded Ni/Ti and VACNT. In addition, the matching degree of the phonon state density (PDOS) at the Ni-VACNT interface increases with increasing contact area between the Ni atoms and Cu substrate. Nevertheless, it was found that over-strong interfacial interaction between the VACNT and Ti element deteriorates the matching degree of high-frequency phonons at the Ti-VACNT interface. These findings offer valuable criteria for designing and selecting materials to enhance interfacial thermal conduction in composite electronic packaging.