To determine the pose relationship between a linear structured light vision sensor and the flange center of an industrial robot, a planar target with only a single circle and its calibration method are designed. The robot's attitude is adjusted such that the laser line passes through the center of the solid circle on the plane target. Through image processing, the pixel coordinates of the center are obtained. After conversion, the coordinates of the center in the sensor coordinate system are obtained. The attitude is adjusted many times, yielding multiple sets of images and the center coordinates of multiple groups of sensors in the sensor coordinate system. The hand-eye matrix is directly solved using the least-squares method based on the corresponding robot pose relationship. The experimental results show that the standard deviation of the three-dimensional coordinates obtained by the proposed method is reduced from 0.3893 mm to 0.2145 mm compared with the hand-eye calibration method using the standard ball as the target, and the root mean square error is effectively reduced with different distances of the same target as the measurement object. This method improves calibration accuracy, does not require expensive targets, and is suitable for field calibration.