We present results of a molecular dynamics study using adaptive intermolecular reactive empirical bond order interatomic potential to analyze thermal transport in three-dimensional pillared single-walled carbon nanotube (SWCNT)–graphene superstructures comprised of unit cells with graphene floors and SWCNT pillars. The results indicate that in-plane as well as out-of-plane thermal conductivity in these superstructures can be tuned by varying the interpillar distance and/or the pillar height. The simulations also provide information on thermal interfacial resistance at the graphene–SWCNT junctions in both the in-plane and out-of-plane directions. Among the superstructures analyzed, the highest effective (based on the unit cell cross-sectional area) in-plane thermal conductivity was 40 W/(m K) with an out-of-plane thermal conductivity of 1.0 W/(m K) for unit cells with an interpillar distance Dx = 3.3 nm and pillar height Dz = 1.2 nm, while the highest out-of-plane thermal conductivity was 6.8 W/(m K) with an in-plane thermal conductivity of 6.4 W/(m K) with Dx = 2.1 nm and Dz= 4.2 nm.