In　the　article　a　new　sparse　low-rank　matrix　decomposition　model　is　proposed　based　on　the　smoothly　clipped　absolute　deviation　(SCAD)　penalty.　In　order　to　overcome　the　computational　hurdle　we　generalize　the　alternating　direction　method　of　multipliers　(ADMM)　algorithm　to　develop　an　alternative　algorithm　to　solve　the　model.　The　algorithm　we　designed　alternatively　renew　the　sparse　matrix　and　low-rank　matrix　in　terms　of　the　closed　form　of　SCAD　penalty.　Thus,　the　algorithm　reduces　the　computational　complexity　while　at　the　same　time　to　keep　the　computational　accuracy.　A　series　of　simulations　have　been　designed　to　demonstrate　the　performances　of　the　algorithm　with　comparing　with　the　Augmented　Lagrange　Multiplier　(ALM)　algorithm.　Ultimately,　we　apply　the　model　to　an　on-board　video　background　modeling　problem.　According　to　model　the　on-board　video　background,　we　can　separate　the　video　background　and　passenger＇s　actions.　Thus,　the　model　can　help　us　to　identify　the　abnormal　action　of　train　passengers.　The　experiments　show　the　background　matrix　we　estimated　is　not　only　sparser,　but　the　computational　efficiency　is　also　improved.