The functional motifs composed of several sequential blocks are difficult to find. Current mining methods might individually find each motif block but fail to connect them with large irregular gaps. In this paper we propose a novel method for the efficient extraction of structured motifs from DNA sequences using multi-objective genetic algorithm. The main advantage of our approach is that a large number of nondominated motifs can be obtained by a single run with respect to conflicting objectives: similarity and support maximization and gap minimization. To the best of our knowledge, this is the first effort in this direction. The proposed method can be applied to any data set with a sequential character. Furthermore, it allows any choice of similarity measures for finding motifs. By analyzing the obtained optimal motifs, the decision maker can understand the tradeoff between the objectives. We compare our method with the two well-known structured motif extraction methods, EXMOTIF and RISOTTO. Experimental results on synthetics data set demonstrate that the proposed method exhibits good performance over the other methods in terms of runtime.