3D LiDARs and cameras are commonly used in the fields of autonomous vehicles, mobile robots and etc. To fuse the complementary information of both, extrinsic calibration is the prerequisite and foundation. Based on the motion characteristics of planar mobile robot, a twostage extrinsic parameter calibration method is proposed in this paper, which can quickly calibrate the extrinsic parameters with the manual intervention as little as possible. In the first stage, the LiDAR odometry and visual odometry are simultaneously estimated in the robot motion process. Then with the extracted translations and rotations, a coarse estimation of the relative rotation is found by using modified Kabsch algorithm.In the second stage, the trihedron formed by three planes of a box is utilized as the marker.Precise extrinsic parameters are obtained by optimizing the distances of projections of points on trihedron edges in the point cloud to corresponding trihedron edges in the image. This efficient algorithm features just less manual intervention for the calibration without any specialized equipments.Finally, the experiment results show that the mean errors on three coordinate axes are only 367, 111 and 078 mm, and the corresponding mean calibration time on the typical mobile computing platform is only about 635 ms.