We investigate the light strip center extraction and system calibration method of a robot line structured light vision measurement system to realize fast on-line measurement of complex objects. First, the model of a robot vision measurement system is established to analyze the key technologies involved for improving the measurement accuracy of the system. Second, on the basis of the traditional gray gravity method, a gray gravity method based on the normal direction is proposed to extract the center of the laser stripe. Considering the influence of camera distortion, the accuracy of extracting the center stripe can be further improved. Third, a two-dimensional checkerboard is applied to synchronously calibrate the camera parameters, laser plane parameters, and hand-eye relationship of the robot, thus improving the efficiency and accuracy of system calibration. Finally, three-dimensional topography and the geometric dimensions of a complex part are measured by the constructed system with high accuracy. The experimental results show that the average measurement error is <0.2  mm and the measurement accuracy is <1.3  %  , indicating that the system can be effectively used in actual industrial measurement.