The　state-of-the-art　High　Efficiency　Video　Coding　(HEVC)　standard　adopts　a　hierarchical　coding　structure　to　improve　its　coding　efficiency.　This　allows　for　the　quantization　parameter　cascading　(QPC)　scheme　that　assigns　quantization　parameters　(Qps)　to　different　hierarchical　layers　in　order　to　further　improve　the　rate-distortion　(RD)　performance.　However,　only　static　QPC　schemes　have　been　suggested　in　HEVC　test　model,　which　are　unable　to　fully　explore　the　potentials　of　QPC.　In　this　paper,　we　propose　an　adaptive　QPC　scheme　for　an　HEVC　hierarchical　structure　to　code　natural　video　sequences　characterized　by　diversified　textures,　motions,　and　encoder　configurations.　We　formulate　the　adaptive　QPC　scheme　as　a　nonlinear　programming　problem　and　solve　it　in　a　scientifically　sound　way　with　a　manageable　low　computational　overhead.　The　proposed　model　addresses　a　generic　Qp　assignment　problem　of　video　coding.　Therefore,　it　also　applies　to　group-of-picture-level,　frame-level　and　coding　unit-level　Qp　assignments.　Comprehensive　experiments　have　demonstrated　that　the　proposed　QPC　scheme　is　able　to　adapt　quickly　to　different　video　contents　and　coding　configurations　while　achieving　noticeable　RD　performance　enhancement　over　all　static　and　adaptive　QPC　schemes　under　comparison　as　well　as　HEVC　default　frame-level　rate　control.　We　have　also　made　valuable　observations　on　the　distributions　of　adaptive　QPC　sets　in　the　videos　of　different　types　of　contents,　which　provide　useful　insights　on　how　to　further　improve　static　QPC　schemes.