This work proposes a three dimensional (3D) robot grasp pose generation method for robot manipulator from the predicted two dimensional (2D) anchors and the depth information of local surface. Compared to the traditional image based grasp area detection methods in which the grasp pose are only presented by two contacts, the proposed method is able to generate more accurate 3D grasp pose. Furthermore, different from the 6-DoF object pose regression methods in which the point cloud of the whole objects is considered, the proposed method is very lightweight, since the 3D computation is only processed on the depth information of the local grasp surface. The method consists of three steps: (1) detecting the 2D grasp anchor and extracting the local grasp surface from image; (2) obtaining the normal vector of the objects’ local grasp surface from the objects’ local point cloud; (3) generating the 3D grasp pose from 2D grasp anchor based on the normal vector of local grasp surface. The experiments are carried on the Cornell and Jacquard grasp datasets. It is found that the proposed method yields improvement on the grasp accuracy compared to the state-of-art 2D anchor methods. And the proposed method is also validated on the practical grasp tasks deployed on a UR5 arm with Robotiq Grippers F85. It outperforms the state-of-art 2D anchor methods on the grasp success rate for dozens of piratical grasp tasks.