Cryogenic　turbo-expander　is　most　significant　equipment　to　provide　cooling　energy　in　system　and　its　working　condition　is　always　deviated　from　design　point.　A　mathematic　prediction　method　study　is　carried　out　to　estimate　turbo-expander　off-design　performance.　Computational　iterative　loop　is　compiled　by　Matlab,　dimensionless　mass　flow　rate　equation　of　mean　streamline　and　novel　loss　correlation　are　applied　to　quantitatively　describe　the　flow　expansion　through　turbine　ducts.　Cryogenic　turbo-expander　performance　is　evaluated　by　total-to-static　efficiency.　According　to　velocity　ratio,　the　effect　of　pressure　ratio,　inlet　temperature,　rotational　speed　variation　to　turbine　performance　is　analyzed,　and　the　predicted　performance　map　is　plotted.　Meanwhile,　an　experimental　study　is　conducted　under　off-design　condition.　Temperature,　pressure,　rotation　speed　and　volume　flow　rate　are　collected,　total-to-static　efficiency　are　calculated　from　turbine　inlet　and　outlet　states　over　pressure　ratio　range　of　2.4-3.4,　and　the　tested　rotation　speed　range　is　set　from　52,000　to　60,000　rpm.　Turbine　efficiency　in　different　pressure　ratio　range　are　categorized　and　plotted　with　velocity　ratio　to　validate　against　computational　predicted　characteristic.　With　experimental　comparison,　this　off-design　performance　mathematic　code　can　predict　turbine　real　operation　well.