In　this　work,　a　new　extended　integrable　(2+1)-dimensional　Kadomtsev-Petviashvili　equation　is　proposed　and　investigated,　which　models　slowly　varying　perturbation　wave　in　dispersion　fluids.　First,　the　WTC-Kruskal　algorithm　is　applied　to　exploring　the　corresponding　compatibility　condition　for　this　equation　in　Painleve　sense.　Then,　N-soliton,　periodic,　breather　solution　as　well　as　the　mixed　form　composing　of　breather　and　soliton(s)　have　been　derived　via　Hirota　bilinear　method　and　symbolic　computation.　Moreover,　we　have　derived　the　rational　and　semi-rational　solutions　in　terms　of　＂long　wave＂limit.　The　rational　solutions　can　be　classified　as　first　order　line　rogue　waves　and　lumps,　while　the　semi-rational　solutions　have　the　forms:　a　hybrid　of　first　order　line　rogue　wave　and　one　soliton,　a　hybrid　of　second　order　line　rogue　wave　and　one　soliton,　a　hybrid　of　lump　and　soliton(s),　a　hybrid　of　lump　and　breather,　a　hybrid　of　lump　and　periodic　solution.