The　two-phase　turbo-expanders　are　in　more　popular　as　their　advantage　of　more　provided　cooling　capacity　in　cryogenic　applications.　However,　it　makes　the　preliminary　or　alternative　design　and　off-design　prediction　for　this　type　turbine　to　remain　an　unworked　area,　due　to　a　lack　of　better　understanding　for　machine　performance　under　two-phase　conditions.　This　paper　numerically　studies　the　machine　off-design　performance　based　on　a　cryogenic　turbo-expander,　which　is　a　key　equipment　to　supply　main　cooling　capacity　for　an　air　separation　plant.　The　investigative　off-design　conditions　including　420　numerical　cases　cover　both　superheated　region　and　two-phase　region.　The　simulations　of　gas　expansion　involving　two-phase　flow　in　nozzle　and　impeller　are　performed　on　nonequilibrium　condensation　model　of　ANSYS　CFX.　According　to　the　state　of　gas　expansion　end　point,　the　numerical　results　could　be　categorized　as　three　types,　i.e.　superheated,　supercooled　and　spontaneous　condensation　expansions.　The　effect　of　non-equilibrium　thermodynamic　process　on　the　outlet　parameters　also　is　revealed　via　comparison　with　results　from　ideal　equilibrium　condensation　model.　Moreover,　the　turbo-expander　performance　maps　under　superheated　and　two-phase　conditions,　including　mass　flow　rate,　degree　of　reaction　and　total-tostatic　efficiency,　are　compared　and　analyzed.　Finally,　taking　liquid　mass　fraction　as　a　fundamental　parameter　as　well　as　velocity　ratio,　new　3-D　performance　maps　of　reaction　and　efficiency　are　developed.　The　research　achievements　could　be　applicable　to　turbine　design　and　performance　prediction　at　two-phase　conditions.