The longest common subsequence problem is classical string problem. It has applications, for example, in pattern recognition and bioinformatics. In this work we present a so-called Beam-ACO approach for solving this problem. Beam-ACO algorithms are hybrid techniques that results from a combination of ant colony optimization and beam search, which is an incomplete branch and bound derivative. Our results show that Beam-ACO is able to find new best solutions for 31 out of 60 benchmark instances that we chose for the experimental evaluation of the algorithm.