Grasping unknown objects is a crucial necessity for robots that operate in an unstructured environment. In this paper, we propose a novel grasping algorithm that uses active vision as basis. The algorithm uses the curvature information obtained from the silhouette of the object. By maximizing the curvature value, the pose of the robot is updated and a suitable grasping configuration is achieved. The algorithm has certain advantages over the existing methods: It does not require a 3D model of the object to be extracted, and it does not rely on any knowledge base obtained offline. This leads to a faster and still reliable grasping of the target object in 3D. The performance of the algorithm is examined by simulations and experiments, and successful results are obtained.