Over the past decades, various methods for comparing the means of two log-normal have been proposed. Some of them are differing in terms of how the statistic test adjust to accept or to reject the null hypothesis. In this study, a new method of test for comparing the means of two log-normal populations is given through the generalized measure of evidence to have against the null hypothesis. However calculations of this method are simple, we find analytically that the considered method is doing well through comparing the size and power statistic test. In addition to the simulations, an example with real data is illustrated.