In order to measure the three-dimensional shape of a non-cooperative target in a close distance in the missions for space targets operations, a line structured-light three-dimensional shape measurement system based on laser triangulation with auto-synchronous scanners was designed. The principle and the configuration of the system were presented and the line structured-light scanners system model was derived. The prototype system was set up and calibrated with a chessboard. The groove board and Tiangong-1 scale model were measured. The measurement results show that the precision of the spatial coordinates measurement is better than 1 mm, the precision of Z coordinates measurement is 0.18 mm, and the average errors of the distance between the measuring points and the fitted plane are 0.31 mm at the distance of 1 m. The system can simplify the scanner and reduce the weight and power consumption, and can be used for the rapid three-dimensional shape measurement in the space missions.