Fast and robust product assembly stage recognition is a key step in human–machine cooperative assembly. To solve the recognition problem of similar adjacent assembly stages, a marker-less assembly stage recognition method is proposed based on corner feature between an assembling product and a digital model. Considering the geometric features of mechanical products, a corner identification method is proposed based on the circumferential angle difference (CADF). Then a corner matching method based on distance constraint is studied for ICP registration to realize the point cloud registration between the product and digital model. Based on the registration relationship, a similarity algorithm based on proximity point proportion is used to calculate the similarity between models and the input assembling product. The model with the greatest similarity is taken as the stage recognition result. In experiments on four group assembling products, the average stage recognition accuracy is 96.15%, which indicates that the proposed method can solve the stage recognition problem. The corner identification method based on the CADF outperforms the Harris-3D corner detection method in the efficiency of assembly stage recognition.