Compressive X-ray tomosynthesis is a computational imaging technique used to reconstruct three-dimensional objects from a set of projection measurements, where the masks are used to modulate the structured illumination to reduce the radiation dose while retaining the reconstruction performance. This paper proposes a conveyor X-ray tomosynthesis imaging method with optimized structured sequential illumination. Variations of this geometry where the object is static but the measurement gantry is dynamic are possible within the proposed framework. In this system, several X-ray sources are successively used to interrogate the moving object lying on a conveyor, where the compressive measurements are received by a set of low-cost strip detectors. The dynamic imaging model and reconstruction framework of the proposed system are established taking into account sensing geometry along with the movement of the object. Subsequently, a genetic algorithm is developed to optimize the exposure sequence of X-ray sources and mask patterns and during the dynamic measurement process. The optimization problem is formulated based on the restricted isometry property of compressive sensing theory to ameliorate the ill-posed inverse tomosynthesis problem. The optimized structured sequential illumination is proved to significantly improve the imaging performance of the conveyor X-ray tomosynthesis system based on a set of simulations.