The effect of the different geometrical dimensionality of two dimensional graphene nanosheets (2D GNSs) and one dimensional carbon nanotubes (1D CNTs) on the non-isothermal crystallization of an ethylene-vinyl acetate (EVA) copolymer at high loading (5 wt%) was studied. Transmission electron microscopy indicated a homogeneous dispersion of GNSs and CNTs in EVA obtained by a solution dispersion process. Fourier-transform infrared spectroscopy and differential scanning calorimetry measurements showed that 1D CNTs and 2D GNSs acted as effective nucleating agents, with a noticeably increased onset crystallization temperature of EVA. A high weight fraction of nano-fillers slowed the overall crystallization rate of composites. At the same crystallization temperatute, the crystallization behavior of GNS/EVA composites was slowed compared to that of the CNT/EVA ones owing to larger nucleus barrier and activation energy of diffusion. Dynamic mechanical relaxation and rheology behavior of CNT/EVA and GNS/EVA composites demonstrated that the planar structure of the GNSs had an intensively negative effect on EVA chain mobility due to interactions between nano- fillers and polymer chains, as well as spatial restriction.