The current state-of-the-art lithium-ion batteries (LIBs) still suffer from severely sluggish kinetics due to their inferior solid-state Li⁺ diffusion and poor conductivity. Rational design of the anode materials with three-dimensional (3D) interconnected nanostructures and conductive skeletons, especially with ordered mesopore architectures, is of paramount importance for LIBs. Herein, 3D bicontinuous cubic, ordered, conductive frameworks of cobalt nitride (om-CoN) are designed and used as anodes for LIBs. The 3D grid-like ordered mesopores (∼7.5 nm) and their very thin (<6 nm) and conductive skeletons in om-CoN simultaneously permit the enhanced Li⁺ permeability/diffusivity and smooth electron transfer for fast kinetics. Favorable thermodynamics and fast kinetics were confirmed by the galvanostatic intermittent titration technique and higher ratio of ion-diffusion capacity contribution and larger Li⁺ diffusion coefficients from cyclic voltammetry tests for om-CoN. As a result, it delivers a large capacity, a high rate capability and a stable specific capacity of 710 mA h g^-1 after 350 cycles at 1 A g^-1, far outperforming nonporous and disordered mesoporous CoN and the previously reported CoN, highlighting the significance and effectiveness of 3D ordered mesopores and conductivity for achieving high-performance Li storage.