In this paper we propose a Beam-ACO approach for a combinatorial optimization problem known as the repetition-free longest common subsequence problem. Given two input sequences x and y over a finite alphabet S, this problem concerns to find a longest common subsequence of x and y in which no letter is repeated. Beam-ACO algorithms are combinations between the metaheuristic ant colony optimization and a deterministic tree search technique called beam search. The algorithm that we present is an adaptation of a previously published Beam-ACO algorithm for the classical longest common subsequence problem. The results of the proposed algorithm outperform existing heuristics from the literature.