The incidence of dengue has increased rapidly in Bangladesh since 2010 with an outbreak in 2018 reaching a historically high number of cases, 10,148. A better understanding of the effects of climate variability before dengue season on the increasing incidence of dengue in Bangladesh can enable early warning of future outbreaks. We developed a generalized linear model to predict the number of annual dengue cases based on monthly minimum temperature, rainfall and sunshine prior to dengue season. Variable selection and leave-one-out cross-validation were performed to identify the best prediction model and to evaluate the model’s performance. Our model successfully predicted the largest outbreak in 2018, with 10,077 cases (95% CI: [9,912–10,276]), in addition to smaller outbreaks in five different years (2003, 2006, 2010, 2012 and 2014) and successfully identified the increasing trend in cases between 2010 and 2018. We found that temperature was positively associated with the annual incidence during the late winter months (between January and March) but negatively associated during the early summer (between April and June). Our results might be suggest an optimal minimum temperature for mosquito growth of 21–23° C. This study has implications for understanding how climate variability has affected recent dengue expansion in neighbours of Bangladesh (such as northern India and Southeast Asia).