Dengue has been as an endemic with year-round presence in Singapore. In the recent years 2013, 2014, and 2016, there were several severe dengue outbreaks, posing serious threat to the public health. To proactively control and mitigate the disease spread, early warnings of dengue outbreaks, at which there are rapid and large-scale spread of dengue incidences, are extremely helpful. In this study, a two-step framework is proposed to predict dengue outbreaks and it is evaluated based on the dengue incidences in Singapore during 2012 to 2017. First, a generalized additive model (GAM) is trained based on the weekly dengue incidence data during 2006 to 2011. The proposed GAM is a one-week-ahead forecasting model, and it inherently accounts for the possible correlation among the historical incidence data, making the residuals approximately normally distributed. Then, an exponentially weighted moving average (EWMA) control chart is proposed to sequentially monitor the weekly residuals during 2012 to 2017. Our investigation shows that the proposed two-step framework is able to give persistent signals at the early stage of the outbreaks in 2013, 2014, and 2016, which provides early alerts of outbreaks and wins time for the early interventions and the preparation of necessary public health resources. In addition, extensive simulations show that the proposed method is comparable to other potential outbreak detection methods and it is robust to the underlying data-generating mechanisms.