In order to ascertain the effect of carbon networks with various dimension on the Li-storage properties of Fe3O4 anode material, three Fe3O4-based nanocomposites with different dimensional carbon networks, including zero-dimensional C/Fe3O4 (0D-C/F), one-dimensional carbon nanotubes/Fe3O4 (1D-CNTs/F) and two-dimensional graphene/Fe3O4 (2D-G/F) nanocomposites, are successfully prepared via precisely controlling the preparation processes and parameters. Their morphology, conductivity, reaction kinetics, and electrochemical properties are discussed in detail. The results show that the addition of 1D-CNTs or 2D-G in the Fe3O4 results in a smaller size of Fe3O4 particles, which shortens the diffusion distance of Li+, and provides a faster electron conduction pathways, as well as the flexible carbon networks will effectively relieve the internal strain during charge and discharge processes. Most importantly, it is revealed that 2D-G/F with the large surface area leads to a faster electrochemical reaction kinetic which is mainly controlled by pseudocapacitive behavior, while the electrochemical reaction kinetic of 1D-CNTs/F is dominated by the slow Li+ insert process. As a result, 2D-G/F shows the best Li-storage performance with a reversible capacity of 1014 mAh g(-1) in the first cycle at 0.1 C and even at a high rate of 5 C, the reversible capacity is still 513.5 mAh g(-1). Furthermore, after 100 cycles at 0.5 C, it still delivers a reversible capacity of 1125.6 mAh g(-1) without capacity decay. (c) 2018 Elsevier Ltd. All rights reserved.