A message-passing algorithm for motif finding is presented. Motif finding stands for the problem of identifying a collection of common subsequences within a given set of DNA sequences. Using a combinatorial framework for this problem, this paper describes it in terms of a graphical model. Subsequently, an inference problem is formulated over this graphical representation for the motif finding problem. The paper develops a message-passing algorithm to efficiently solve this graph-based inference problem. This algorithm serves as an efficient heuristic for solving what is otherwise a computationally intensive combinatorial optimization problem.