Fast Li-ion conductivity at room temperature is a major challenge for utilization of all-solid-state Li batteries. Metal borohydrides with neutral ligands are a new emerging class of solid-state ionic conductors, and here we report the discovery of a new mono-methylamine lithium borohydride with very fast Li+ conductivity at room temperature. LiBH4⋅CH3NH2 crystallizes in the monoclinic space group P21/c, forming a two-dimensional unique layered structure. The layers are separated by hydrophobic −CH3 moieties, and contain large voids, allowing for fast Li-ionic conduction in the interlayers, σ(Li+)=1.24×10−3 S cm−1 at room temperature. The electronic conductivity is negligible, and the electrochemical stability is ≈2.1 V vs Li. The first all-solid-state battery using a lithium borohydride with a neutral ligand as the electrolyte, Li-metal as the anode and TiS2 as the cathode is demonstrated.