Autonomous vision-based aerial grasping is an essential and challenging task for aerial manipulation missions. In this paper, we propose a vision-based aerial grasping system for a Rotorcraft Unmanned Aerial Vehicle (UAV) to grasp a target object. The UAV system is equipped with a monocular camera, a 3-DOF robotic arm with a gripper and a Jetson TK1 computer. Efficient and reliable visual detectors and control laws are crucial for autonomous aerial grasping using limited onboard sensing and computational capabilities. To detect and track the target object in real time, an efficient proposal algorithm is presented to reliably estimate the region of interest (ROI), then a correlation filter-based classifier is developed to track the detected object. Moreover, a support vector regression (SVR)-based grasping position detector is proposed to improve the grasp success rate with high computational efficiency. Using the estimated grasping position and the UAV?Äôs states, novel control laws of the UAV and the robotic arm are proposed to perform aerial grasping. Extensive simulations and outdoor flight experiments have been implemented. The experimental results illustrate that the proposed vision-based aerial grasping system can autonomously and reliably grasp the target object while working entirely onboard.