For　the　inverse　proposition　design　of　a　three-dimensional　centrifugal　impeller　using　the　streamline　curvature　method,　the　cubic　spline　curve　fitting　method　is　extensively　used　to　solve　the　velocity　gradient　equation.　Given　the　deficiency　in　stability　with　the　cubic　spline　curve　fitting　method,　a　new　finite　difference　method　is　proposed　to　solve　the　velocity　gradient　equation　on　the　S2m　stream　surface.　In　the　finite　difference　scheme,　the　relative　velocity　derivative　along　the　streamline　direction　is　decomposed　into　two　terms.　One　term　uses　forward　difference,　and　the　other　uses　backward　difference.　The　difference　schemes　of　all　other　parameter　derivatives　in　the　velocity　gradient　equation　adopt　forward　difference.　The　method　can　guarantee　the　matrix　main　diagonal　elements　of　the　dominant,　indicating　stable　convergence　in　solving　the　velocity　field.　Robustness　analysis　is　performed　for　both　methods,　and　the　new　finite　difference　method　shows　excellent　superiority　in　stability.　Finally,　the　finite　difference　method　is　applied　to　redesign　the　Krain　impeller.　Through　computational　fluid　dynamics,　the　efficiency　of　the　redesigned　impeller　at　the　design　operating　point　is　increased　by　approximately　0.3%　and　the　pressure　ratio　by　approximately　5%.　These　results　show　that　the　difference　method　is　feasible　to　solve　the　S2m　stream　surface　velocity　gradient　equation.