The automated tape placement and the automated fiber placement (AFP) machines provide a safer working environment and reduce the labor intensity of workers than the traditional manual fiber placement does. Thus, the production accuracy, repeatability and efficiency of composite manufacturing are significantly improved. However, the current AFP systems can only produce the composite components with large open surface or simple revolution parts, which cannot meet the growing interest in small complex or closed structures from industry. In this research, by employing a 1-degree of freedom (DoF) rotational stage, a 6-RSS parallel robot, and a 6-DoF serial robot, the dexterity of the AFP system can be significantly improved for manufacturing complex composite parts. The rotational stage mounted on the parallel robot is utilized to hold the mandrel and the serial robot carries the placement head to mimic two human hands that have enough dexterity to lay the fiber to the mandrel with complex contour. Although the CCM system increases the flexibility of composite manufacturing, it is quite time-consuming or even impossible to generate the feasible off-line path, which ensures uniform lay-up of subsequent fibers considering the constraints like singularities, collisions between the fiber placement head and mandrel, smooth fiber direction change and keeping the fiber placement head along the norm of the part's surface, etc. Moreover, due to the existing positioning error of the robots, the on-line path correction is needed. Therefore, the on-line pose correction algorithm is proposed to correct the paths of both parallel and serial robots, and to keep the relative path between the two robots unchanged through the visual feedback when the constraint or singularity problems in the off-line path planning occur. The experimental results demonstrate the designed CCM system can fulfill the movement needed for manufacturing a composite structure with Y-shape.