Existing methods of hand-eye calibration between robot and 2D light detection and ranging （LiDAR） generally have shortcomings such as high cost of calibration instrument manufacture， strict requirement of sampling process， etc. To address these problems， a method using a calibration instrument with orthogonal corner feature was proposed. During the calibration process the calibration instrument was kept a fixed pose in robot base frame. When the robot mounted with the LiDAR was controlled to scan the calibration instrument， there are three intersection lines among the LiDAR’s scanning plane and three calibration planes. Using the geometric constraints among three lines， the transformation between LiDAR and calibration frame was computed. From changing the robot pose and repeptively scanning， a constraint equation with respect to the transformation matrix between LiDAR and robot end-effector frame was built. The transformation matrix estimation was acquired from solving the constraint equation. A hand-eye calibration optimization method based on planar features was also proposed. It is a three-stage iteration process. The optimization method avoids side effects from calibration instrument manufacture errors. The experimental results showed in the condition that the LiDAR scanning error was 2 mm， in 10 iterations the Euler angles error of the estimated rotation matrix was less than 0.01°， and the distance error of the translation vector was less than 1.0 mm. Comparing to another method under the same calibration conditions， the proposed method has an advantage in convergence speed， and is also more objective and reasonable in the choice of initial values.