Phylogenetics has gained in public favor for the analysis of DNA sequence data as molecular biology has advanced. Among a number of algorithms for phylogenetics, the fastDNAml is considered to have reasonable computational cost and performance. However, it has a defect that its performance is likely to be significantly affected by the order of taxon addition. In this paper, we propose a genetic algorithm for optimizing the order of taxon addition in the fastDNAml. Experimental results show that the fastDNAml with the optimized order of taxon addition constructs more probable evolutionary trees in terms of the maximum likelihood.