The use of electric buses (EBs) can help reduce vehicle emissions and improve our environment. However, it brings new challenges in transit operations due to the limited driving range of EBs. This study proposes a new mathematical programming model for optimizing the single-line EB vehicle scheduling by considering the use of a skip-stop operation strategy. The objective of the model is to minimize both operator cost and passenger cost. A genetic algorithm is proposed to solve the model and generate the quasi-optimal results, including the required fleet size, vehicle trip chains, charging decisions, and stopping and stop-skipping plans. A case study of a real-world bus line in the city of Dandong, China, is conducted. The experimental results show that compared to using a full-stop strategy, the use of a skip-stop strategy can reduce the total system cost by 15.09% and improve the average energy utilization rate by 9.02%.