Due　to　the　existence　of　measurement　error　and　approximate　theory　of　network　model　parameters,　the　result　of　power　system　state　estimation　is　uncertain.　Interval　analysis　based　on　iterative　solution　method　can　estimate　the　upper　and　lower　bounds　of　system　state　variables,　but　the　accuracy　of　estimation　will　be　affected　by　interval　expansion.　In　this　paper,　using　a　recursive　solution　method,　an　interval　state　estimation　method　for　power　system　based　on　holomorphic　embedding　method　is　proposed.　By　introducing　the　holomorphic　embedding　method,　the　interval　measurement　equation　is　embedded　and　reconstructed,　and　the　coefficient　recursion　formula　after　power　series　expansion　is　obtained,　which　is　solved　in　recursive　form,　and　the　interval　solution　of　state　quantity　is　obtained.　Cases　show　that,　compared　with　the　Monte　Carlo　simulation　method,　the　proposed　method　is　effective　and　can　reduce　the　calculation　time　greatly.　©　2023　IEEE.