The identification of the key factors influencing dengue occurrence is critical for a successful response to the outbreak. It was interesting to consider possible differences in meteorological factors affecting dengue incidence during epidemic and non-epidemic periods. In this study, the overall correlation between weekly dengue incidence rates and meteorological variables were conducted in southern Taiwan (Tainan and Kaohsiung cities) from 2007 to 2017. The lagged-time Poisson regression analysis based on generalized estimating equation (GEE) was also performed. This study found that the best-fitting Poisson models with the smallest QICu values to characterize the relationships between dengue fever cases and meteorological factors in Tainan (QICu = −8.49 × 10−3) and Kaohsiung (−3116.30) for epidemic periods, respectively. During dengue epidemics, the maximum temperature with 2-month lag (β = 0.8400, p < 0.001) and minimum temperature with 5-month lag (0.3832, p < 0.001). During non-epidemic periods, the minimum temperature with 3-month lag (0.1737, p < 0.001) and mean temperature with 2-month lag (2.6743, p < 0.001) had a positive effect on dengue incidence in Tainan and Kaohsiung, respectively.