Hurricanes can cause severe property damage and casualties in coastal regions. Diesel fuel plays a crucial role in hurricane disaster relief. It is important to optimize fuel supply chain operations so that emergency demand for diesel can be mitigated in a timely manner. However, it can be challenging to estimate demand for fuel and make informed proactive and reactive decisions in the distribution process, accounting for the hurricane's path and severity. We develop predictive and prescriptive models to guide diesel fuel supply chain operations for hurricane disaster relief. We construct a model for estimating diesel fuel demand from historical weather forecasts and power outage data. This predictive model feeds into a prescriptive stochastic programming model implemented in a rolling-horizon fashion to dispatch tank trucks. This data-driven optimization tool provides a framework for decision support in preparation for approaching hurricanes, and our numerical results provide insights regarding key aspects of operations.