This paper presents the research and development of an imaging order scheduler for FORMOSAT-2, an Earth observation satellite taking images of ocean and landmass in the vicinity of Taiwan according to customers' requests. The quality of satellite image pictures depends heavily on the posture and position of the spacecraft as well as on the weather condition of the target area when taking the images. The satellite imaging order scheduler considers current and future weather conditions to provide an imaging plan that satisfies customer requirements with quality imaging pictures. The satellite imaging order scheduling problem is formulated as a stochastic integer programming problem. We adopt the rolling horizon approach to solve this problem. A nominal plan is generated based on the forecast weather conditions. This nominal plan is adjusted with the updated information during its execution. Lagrangian relaxation is used to solve for a nominal imaging plan. Numerical results indicate that our imaging order scheduler is effective and efficient to generate good imaging plans for realistic problems. We also conduct experiments to further explore the algorithmic features. Our analysis of variance (ANOVA) study concludes that the performance of our solution algorithm significantly depends on the number of jobs, as well as the rewards of order completion. However, the effect caused by weather conditions is not obvious.