In man–machine cooperative assembly, assembly recognition that determines the current manual working stage is key information to driving automatic computer-aided assistance. Focused on three features of the assembly scene—movable view, process stage, and CAD model template— a view-free and marker-less assembly stage recognition method is proposed in this paper. By constructing the semantic model for the assembly scene and the stage model for CAD parts, a depth image of assembly and a CAD model can be extracted as point clouds. Then we propose the segmented projection contour descriptor to uniformly express the shape information as a series of contours, so the 3D registration issue is converted to a 2D registration issue. The vertex-to-edge Hausdorff distance is proposed in the partial registration to determine the transformation matrix for each pair of contours. Finally, the overall matching algorithm based on the overlay ratio is given, and the best matching stage model indicates the current assembly stage. The recognition and classification experiments are carried out to verify the proposed method. A comparison with traditional Hausdorff distance proves the proposed algorithm performs better in stage recognition. Our study reveals that the proposed view-free and marker-less method can solve the stage recognition issue based on the assembly’s depth image, so as to connect the on-site assembly with the digital information.