With the development of the global economy, the demand for manufacturing is increasing. Accordingly, human–robot collaborative assembly has become a research hotspot. This paper aims to solve the efficiency problems inherent in traditional human-machine collaboration. Based on eye–hand and finite state machines, a collaborative assembly method is proposed. The method determines the human’s intention by collecting posture and eye data, which can control a robot to grasp an object, move it, and perform co-assembly. The robot’s automatic path planning is based on a probabilistic roadmap planner. Virtual reality tests show that the proposed method is more efficient than traditional methods.