Safe fast-charging lithium-ion batteries (LIBs) have huge potential market size on demand according to their shortened charging time for high-power devices. Zero-strain spinel Li4Ti5O12 is one of ideal candidates for safe high-power batteries owing to its good cycling performance, low cost and safety. However, the inherent insulating characteristic of LTO seriously limits its high-rate capability. In this work, we successfully synthesize novel wavelike spinel LTO nanosheets using a facile 'co-hydrolysis' method, which is superior to molten-salt approach and traditional solvothermal method in some respects. The unique 2D structures have single-crystal framework with shortened path for Li ion transport. As a result, the N-doped 2D wavelike LTO with 0.6 wt.% of 'carbon joint' not only exhibits exciting capacity of ~180 and ~150 mA h g(-1) for fast lithium storage at high discharge/charge rates of 1.7 and 8.5 A g(-1) (10C and 50C) respectively, but also shows excellent low-temperature performance at -20°C. In addition, the cost may be further decreased due to recycled functional reagents. This novel nanostructured 2D LTO anode material makes it possible to develop safe fast-charging high-power lithium ion batteries.