It is known that the interlayer van der Waals (vdW) interactions will decrease the thermal conductivity of graphene. Single layer graphene (SLG) has the highest thermal conductivities, double layer graphene (DLG) would decrease to about half of the thermal conductivity of SLG. The graphite was measured to have a thermal conductivity of about 2000 W/m-K. Some research shows that graphite differs from SLG within a factor of 2, and DLG has almost the same thermal conductivity with graphite. In theoretical aspect, how to simulate the vdW interaction between graphene layers is a long existing problem. It is only until recently that the vdW interaction is still an active topic in first principle calculations. The popular methods include the Grimme’s DFT-D, vdW-DF and vdW-DFT-R methods. The vdW-DFT-R method was further optimized to increase accuracy by Hamada and was found to predict the most accurate interlayer distance between AB-stacked graphene in our recent study. The motivation of this work is to investigate the effect of vdW interaction on the thermal conductivity of multiple layer graphene from principles. We will calculate firstly the phonon dispersion relations of multiple layer graphene with the vdW interaction included. The obtained phonon properties and force constants will be combined with the ShengBTE method to calculate the thermal conductivity. The results show how vdW interaction causes the dimensional crossover of graphene thermal conductivity.