In this paper, we present a stochastic drone-scheduling problem where the energy consumption of drones between any two nodes is uncertain. Considering uncertain energy consumption as opposed to deterministic energy consumption can effectively enhance the safety of drone flights. To address this issue, we developed a two-stage stochastic programming model with recourse cost, and we employed a fixed-sample sampling strategy based on Monte Carlo simulation to characterize uncertain variables, followed by the design of an efficient variable neighborhood search algorithm to solve the model. Case study results indicate the superiority of our algorithm over genetic algorithms. Additionally, a comparison between deterministic and stochastic models suggests that considering the uncertainty in energy consumption can significantly enhance the average returns of unmanned aerial vehicle scheduling systems.