We report a simple one-pot solvothermal method of a FeS2/CNT (carbon nanotube) neural network nanostructure composite (FeS2/CNT-NN) that exhibits outstanding electrochemical performance as a sodium-ion battery anode. In these composites, uniform microspheres assembled from FeS2 nanoparticles act as “somas” and CNTs act as “neurites”. The weight ratio of FeS2 to CNTs affects not only the composite morphology, but also the sodium-ion storage performance. By optimizing this ratio, we achieve stable capacities up to 394 mA h g−1 after 400 cycles at 200 mA g−1. Most impressively, when the current densities are increased, excellent capacity and stability are maintained. At 1 A g−1 to 22 A g−1, surprisingly high capacities of 309 mA h g−1 to 254 mA h g−1 are maintained after 1800 cycles and 8400 cycles, respectively. The excellent electrochemical performance has been found to originate from the unique neural network structure, which offers high surface area and small FeS2 particle size for sufficient sodiation and desodiation, and enough room and mechanical integrity for volume expansion. Pseudocapacitance has also been found to dominate in the redox reactions, accounting for the outstanding rate and cycling performance. The excellent charge-discharge performance shows that FeS2/CNT-NN composites are promising candidates for rechargeable sodium-ion batteries.