A　key　challenge　for　potassium-ion　batteries　is　to　explore　low-cost　electrode　materials　that　allow　fast　and　reversible　insertion　of　large-ionic-size　K+.　Here,　we　report　an　inorganic-open-framework　anode　(KTiOPO4),　which　achieves　a　reversible　capacity　of　up　to　102mAhg(-1)　(307mAhcm(-3)),　flat　voltage　plateaus　at　a　safe　average　potential　of　0.82V　(vs.　K/K+),　a　long　lifespan　of　over　200　cycles,　and　K+-transport　kinetics　approximate　to　10　times　faster　than　those　of　Na-superionic　conductors.　Combined　experimental　analysis　and　first-principles　calculations　reveal　a　charge　storage　mechanism　involving　biphasic　and　solid　solution　reactions　and　a　cell　volume　change　(9.5%)　even　smaller　than　that　for　Li+-insertion　into　graphite　(approximate　to　10%).　KTiOPO4　exhibits　quasi-3D　lattice　expansion　on　K+　intercalation,　enabling　the　disintegration　of　small　lattice　strain　and　thus　high　structural　stability.　The　inorganic　open-frameworks　may　open　a　new　avenue　for　exploring　low-cost,　stable　and　fast-kinetic　battery　chemistry.