The pursuit of lower costs and the volatility of spot prices force shipping companies to sign fuel supply contracts with suppliers in advance. Meanwhile, suppliers that take on price risks typically seek further information on spot market prices. Furthermore, they need to consider whether to share the information with shipping companies as such information can affect shipping companies' decision on speed and, hence, their fuel consumption and shipper business. To study the refueling and information issues of the shipping supply chain, we describe a game between a shipping company and a supplier on the basis of a fuel supply contract. Results show that compared with the case without information sharing, the case with information sharing with a possibly lower spot price can bring higher profits for the shipping company and supplier. At this point, the shipping company will increase its navigation speed and benefit from the resulting increase in shipper business. Meanwhile, the supplier can benefit from the shipping company's increased fuel consumption. The supplier decides to share information with the shipping company before receiving signals only when the prediction accuracy is high, indicating that the supplier's prediction motivation is to sway the shipping company's risk assessment. Restricted by prediction costs, the supplier will not improve the prediction accuracy indefinitely, but such improvement can always benefit the shipping company. Hence, information prediction can be a win‐win strategy for the shipping company and supplier.