Polynomial　chaos　expansion　(PCE)　is　a　widely　used　approach　for　establishing　the　surrogate　model　of　a　time-consuming　performance　function　for　the　convenience　of　uncertainty　quantification　of　a　stochastic　structure.　However,　it　remains　difficult　to　calculate　the　probability　density　function　(PDF)　of　the　PCE　accurately　for　general　cases,　though　the　PDF,　as　a　complete　representation　of　a　random　variable,　is　often　required　in　some　uncertainty　problems.　To　address　this　problem,　this　paper　proposes　a　semi-analytical　method　to　compute　the　PDF　of　a　PCE.　This　method　derives　the　closed-form　solutions　of　characteristic　functions　(CFs)　of　the　first-　and　second-order　PCEs,　while　an　equivalent　parabolization　technique　is　proposed　to　provide　the　approximate　solutions　of　CFs　of　higher-order　PCEs.　Then,　the　PDF　of　the　PCE　can　be　obtained　by　the　Fourier　transform　of　the　resulting　CF.　Three　numerical　examples　are　investigated　to　demonstrate　the　accuracy,　applicability,　and　efficiency　of　the　proposed　method　for　probability　density　estimation　of　PCE　in　structural　reliability　analysis.　©　2024