In　this　paper,　we　propose　a　modified　proximal　gradient　method　for　a　class　of　sparse　optimization　problems,　which　arise　in　many　contemporary　statistical　and　signal　processing　applications.　The　new　method　uses　a　new　scheme　to　construct　the　descent　direction　based　on　the　proximal　gradient　method.　It　is　proven　that　the　modified　proximal　gradient　method　is　Q-linearly　convergent　without　the　assumption　of　the　strong　convexity　of　the　objective　function.　Numerical　experiments　have　been　conducted　to　evaluate　the　proposed　method.　©　2018　World　Scientific　Publishing　Company.