We propose all efficient method using multi-objective genetic algorithm (MOGAMOD) to discover optimal motifs in sequential data. The main advantage of our approach is that a large number of tradeoff (i.e., nondominated) motifs call be obtained by a single run with respect to conflicting objectives: similarity, motif length and support maximization. To the best of our knowledge, this is the first effort in this direction. MOGAMOD call 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 call understand the tradeoff between the objectives. We compare MOGAMOD with the three well-known motif discovery methods, AlignACE, MEME and Weeder. Experimental results on real data set extracted from TRANSFAC database demonstrate that the proposed method exhibits good performance over the other methods in terms of accuracy and runtime.