A new bandwidth reduction algorithm is developed by combining the two-step approach and the frontal ordering scheme. In the two-step approach, finite elements are numbered first, followed by nodal numbering based on the graph theory. The concept of wave front is incorporated into it to control the cardinality of the set of adjacent nodes and the bandwidth to be achieved. They are controlled systematically by rational selection of next candidates with the purpose of getting the smaller bandwidth efficiently. Eighteen meshes are renumbered and the results are compared with those of well-known algorithms. The results demonstrate the efficiency and the reliability of the proposed algorithm.