© 2019 Elsevier B.V. The effects of natural convection on dendrite morphologies formed during solidification of a three–dimensional (3D) bulk crystal have not been clarified yet. Although numerical simulation is key to solve the problem, it is not straightforward from a computational cost point of view to simulate the growth of multiple dendrites and liquid flow simultaneously. In this study, we numerically investigate the effects of natural convection on the dendrite morphologies formed during 3D upward directional solidification of an Al–3 wt%Cu alloy, providing a comparison with two–dimensional (2D) simulations. Large–scale simulations of a model coupling phase–field and lattice Boltzmann methods are performed by parallel computation using multi graphics processing units on a supercomputer. As a result of a series of simulations where gravity is changed, similar results are obtained in the 3D and 2D simulations: the average primary arm spacing increases as the gravity decreases in the negative region, the large upward flow causes unstable dendrite growth, and the downward flow enhances the growth of secondary arms. On the other hand, because the natural convection caused under gravity is less in the 3D than the 2D case, the effect of natural convection in the 3D bulk is smaller than in the 2D. In addition, due to differences in flow patterns in front of dendrite tips, there are some distinctions in dendrite growth between 2D and 3D cases.