Linearly constrained separable convex minimization problems have been raised widely in many real-world applications. In this paper, we propose a homotopybased 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/(1/k)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.