Increasing grasping efficiency is very important for the robots to grasp unknown objects especially subjected to unfamiliar environments. To achieve this, a new algorithm is proposed based on the C-shape configuration. Specifically, the geometric model of the used under-actuated gripper is approximated as a C-shape. To obtain an appropriate graspable position, this C-shape configuration is applied to fit geometric model of an unknown object. The geometric model of unknown object is constructed by using a single-view partial point cloud. To examine the algorithm using simulations, a comparison of the commonly used motion planners is made. The motion planner with the highest number of solved runs, lowest computing time and the shortest path length is chosen to execute grasps found by this grasping algorithm. The simulation results demonstrate that excellent grasping efficiency is achieved by adopting our algorithm. To validate this algorithm, experiment tests are carried out using a UR5 robot arm and an under-actuated gripper. The experimental results show that steady grasping actions are obtained. Hence, this research provides a novel algorithm for fast grasping of unknown objects.