A　new　active-learning　function　is　developed　to　integrate　Polynomial-Chaos　Kriging　with　probability　density　evolution　method.　First,　the　relative　importance　of　each　representative　point　to　the　probability　of　failure　is　separately　measured,　thereby　the　region　of　interest　is　defined　for　the　probability　density　evolution　method,　which　covers　the　representative　points　exerting　vital　contributions　to　the　probability　of　failure.　Then,　a　new　learning　function　called　the　probability　density　evolution　method-oriented　information　entropy　is　readily　devised　based　on　the　information　theory,　and　the　stopping　condition　is　defined　by　specifying　a　threshold　for　the　learning　function　values.　Two　examples　are　studied　to　show　the　efficacy　of　the　adaptive　Polynomial-Chaos　Kriging　probability　density　evolution　method,　and　the　recommended　values　of　two　key　parameters　associated　with　this　new　learning　function　are　provided.　Moreover,　comprehensive　comparisons　are　conducted　against　several　existing　reliability　methods.　The　results　highlight　the　advantage　of　the　proposed　active-learning　function　for　structural　reliability　analysis　in　terms　of　both　computational　accuracy　and　efficiency.