We report a low‐cost method for the fabrication of three‐dimensional graphene aerogel (3DGA) with an interconnected porous structure by using a simple hydrothermal reaction of graphite oxide (GO) in the presence of treated filter paper and subsequent annealing. In the hydrothermal process, the filter paper prevents GO sheets from intimate layer‐by‐layer stacking and serves as linkers to construct a three‐dimensional structural graphene hydrogel (GH). The pure 3DGA with an interconnected porous structure is achieved through the calcination of the GH with a three‐dimensional network structure. The as‐fabricated 3DGA electrode exhibits an improved lithium storage performance with a capacity of 712.8 mAh g−1 after 200 cycles at a rate of 200 mA g−1. More importantly, the electrode still shows a reversible capacity of 237.1 mAh g−1 even at a high rate of 1600 mA g−1, demonstrating its remarkable rate capability. The excellent electrochemical performance of the 3DGA electrode is ascribed to its distinct interconnected porous nanoarchitecture with exposed defects and edges as well as large specific surface area. The present design concept of 3DGA may provide a novel strategy for the preparation of advanced carbon materials for electrochemical energy storage systems.