Standard methods of using the t-test and the Wilcoxon test have deficiencies for comparing the means of two skewed log-normal samples. In this paper, we propose two new methods to overcome these deficiencies: (1) a likelihood-based approach and (2) a bootstrap-based approach. Our simulation study shows that the likelihood-based approach is the best in terms of the type I error rate and power when data follow a log-normal distribution.