A transport system with curved track pair is constructed for multiple pulsed X-ray source-in-motion to perform fast digital tomosynthesis imaging. It includes a curved rigid track pair with predetermined curvature, a primary motor stage car loaded with X-ray sources and wheels loaded with tension or compression springs. The car is driven by primary motor mounted at base frame and an engaged gear mounted at the car. The car can carry heavy loads, travel with high precision and high repeatability at all installation orientations while motion vibration is minimal. It is also scalable to have a larger radius. Track angle span usually can be from about ten degrees to about 170 degrees. During imaging acquisition, X-ray sources can sweep precisely from one location to another. The car has enough clearance to move in its path without rubbing wheels on tracks.