We　consider　the　linearly　constrained　separable　convex　programming　problem　whose　objective　function　is　separable　into　m　individual　convex　functions　with　non-overlapping　variables.　The　alternating　direction　method　of　multipliers　(ADMM)　has　been　well　studied　in　the　literature　for　the　special　case　m　=　2,　but　the　direct　extension　of　ADMM　for　the　general　case　m　＞=　2　is　not　necessarily　convergent.　In　this　paper,　we　propose　a　new　linearized　ADMM-based　contraction　type　algorithms　for　the　general　case　m　＞=　2.　For　the　proposed　algorithm,　we　prove　its　convergence　via　the　analytic　framework　of　contractive　type　methods　and　we　derive　a　worst-case　O(1/t)　convergence　rate　in　ergodic　sense.　Finally,　numerical　results　are　reported　to　demonstrate　the　effectiveness　of　the　proposed　algorithm.