A new way was proposed to enhance the interfacial thermal conductance (ITC) of silicon carbide (SiC) composite through the overlapped carbon nanotubes (CNTs) and intertube atoms. By nonequilibrium molecular dynamics (NEMD) simulations, the dependence of ITC on both the number of intertube atoms and the temperature was studied. It is indicated that the ITC can be significantly enhanced by adding intertube atoms and finally becomes saturated with the increase of the number of intertube atoms. And the mechanism is discussed by analyzing the probability distributions of atomic forces and vibrational density of states (VDOS). This work may provide some guidance on enhancing the ITC of CNT-based composites.