Graphene, in addition to its unique electronic and optical properties, reveals unusually high thermal conductivity. The fact that the thermal conductivity of large enough graphene sheets should be higher than that of basal planes of bulk graphite was predicted theoretically by Klemens. However, the exact mechanisms behind the drastic alteration of a material's intrinsic ability to conduct heat as its dimensionality changes from two to three dimensions remain elusive. The recent availability of high-quality few-layer graphene (FLG) materials allowed us to study dimensional crossover experimentally. Here we show that the room-temperature thermal conductivity changes from approximately 2,800 to approximately 1,300 W m(-1) K(-1) as the number of atomic planes in FLG increases from 2 to 4. We explained the observed evolution from two dimensions to bulk by the cross-plane coupling of the low-energy phonons and changes in the phonon Umklapp scattering. The obtained results shed light on heat conduction in low-dimensional materials and may open up FLG applications in thermal management of nanoelectronics.