Linearly　constrained　separable　convex　minimization　problems　have　been　raised　widely　in　many　real-world　applications.　In　this　paper,　we　propose　a　homotopy-based　alternating　direction　method　of　multipliers　for　solving　this　kind　of　problems.　The　proposed　method　owns　some　advantages　of　the　classical　proximal　alternating　direction　method　of　multipliers　and　homotopy　method.　Under　some　suitable　conditions,　we　prove　global　convergence　and　the　worst-case　O(1k)　convergence　rate　in　a　nonergodic　sense.　Preliminary　numerical　results　indicate　effectiveness　and　efficiency　of　the　proposed　method　compared　with　some　state-of-the-art　methods.　©　2017,　Operations　Research　Society　of　China,　Periodicals　Agency　of　Shanghai　University,　Science　Press,　and　Springer-Verlag　Berlin　Heidelberg.