In this paper, the thermal boundary resistance and conductive properties of Cu/Al interface are investigated by using first-principles calculations based on density functional theory (DFT) with considering the pressure influence. Based on the atomic model of Cu/Al interface the simulation results show that the lattice parameters for both Cu and Al are sensitive to pressure and density states of Cu/Al interface increase as pressure increases from 0 to 5 GPa. Although Cu and Al have the same atomic structure, the significant differences of the density of phonon states lead to the thermal resistance that exists at the Cu/Al interface. At the Cu/Al interface, Cu and Al atoms can diffuse into each other and form an alloy-like interfacial region. The change of the copper component in the alloy can considerably affect the conductive properties of Cu/Al interface.