Over-dispersion has been well-known often besetting counting data analysis. In this talk, we assume that data follow the quasi-likelihood distribution that the variance is proportional to a known function of the mean, such that the scale parameter captures over-dispersion. When data fit the generalized linear models, we propose the generalized Huber’s condition, under which the root for inference based on quasi-likelihood estimation converges weakly, along with the other regularity conditions. Based on the large-sample approximation, we apply the simultaneous confidence interval method to the Salmonella data obtained from a mutagenicity test, using the proposed theory.