This　paper　proposes　a　new　extended　(3　+　1)-dimensional　Kadomtsev-Petviashvili　equation　that　portrays　a　unique　dispersion　effect　about　x,z$$　x,z　$$.　Its　integrability　is　confirmed　via　the　WTC-Kruskal　algorithm　in　Painleve　sense.　N$$　N　$$-soliton,　breather,　and　O$$　O　$$-type　solitary　wave　are　derived　systematically　at　first.　Then,　the　mixed　solution　composed　of　soliton　and　breather　is　obtained.　In　addition,　the　＂long　wave＂　limit　is　employed　to　construct　rational　and　semi-rational　solution.　The　rational　solution　can　be　classified　as　rogue　wave,　T$$　T　$$-type　solitary　wave,　and　lump　wave.　The　semi-rational　solution　has　the　form　a　hybrid　of　two　solitons,　a　hybrid　of　rogue　wave　and　soliton,　a　hybrid　of　lump　and　soliton(s),　and　a　hybrid　of　lump　and　breather.　The　results　may　help　simulate　complex　waves　and　their　interactions　in　fluid.