This paper presents the effect of interface on the equivalent thermal conductivity of the carbon nanotube composites. The element free Galerkin method has been utilized as a numerical tool to evaluate the thermal conductivity of the composites. The numerical results have been obtained using continuum mechanics approach for a model composite problem, and it was found that the interface has a major effect on the thermal conductivity of the composites. The effect of interface on the effective conductivity of the composite is small for short nanotubes as compared to long nanotubes. Interface thickness also plays an important role on the effective thermal conductivity of the composite. Nanotube anisotropy has got a small effect on effective thermal conductivity of the composites. Transverse thermal conductivity of the composite has got nearly linear variation with nanotube length.