We　propose　an　appealing　line-search-based　partial　proximal　alternating　directions　(LSPPAD)　method　for　solving　a　class　of　separable　convex　optimization　problems.　These　problems　under　consideration　are　common　in　practice.　The　proposed　method　solves　two　subproblems　at　each　iteration:　one　is　solved　by　a　proximal　point　method,　while　the　proximal　term　is　absent　from　the　other.　Both　subproblems　admit　inexact　solutions.　Aline　search　technique　is　used　to　guarantee　the　convergence.　The　convergence　of　the　LSPPAD　method　is　established　under　some　suitable　conditions.　The　advantage　of　the　proposed　method　is　that　it　provides　the　tractability　of　the　subproblem　in　which　the　proximal　term　is　absent.　Numerical　tests　show　that　the　LSPPAD　method　has　better　performance　compared　with　the　existing　alternating　projection　based　prediction-correction　(APBPC)　method　if　both　are　employed　to　solve　the　described　problem.