This paper proposes a novel bin picking framework, two-stage grasping, aiming at precise grasping of cluttered small objects. Object density estimation and rough grasping are conducted in the first stage. Fine segmentation, detection, grasping, and pushing are performed in the second stage. A small object bin picking system has been realized to exhibit the concept of two-stage grasping. Experiments have shown the effectiveness of the proposed framework. Unlike traditional bin picking methods focusing on vision-based grasping planning using classic frameworks, the challenges of picking cluttered small objects can be solved by the proposed new framework with simple vision detection and planning.