Additive manufacturing processes, especially those based on fused filament fabrication (FFF) mechanism, have relatively low productivity and suffer from production scalability issue. One solution is to adopt a collaborative additive manufacturing system that is equipped with multiple extruders working simultaneously to improve productivity. The collaborative additive manufacturing encounters a grand challenge in the scheduling of printing path scanning by different extruders. If not properly scheduled, the extruders may collide into each other or the structures built by earlier scheduled scanning tasks. However, there existed limited research addressing this problem, in particular, lacking the determination of the scanning direction and the scheduling for sub-path scanning. This paper deals with the challenges by developing an improved method to optimally break the existing printing paths into sub-paths and assign these generated sub-paths to different extruders to obtain the lowest possible makespan. A mathematical model is formulated to characterize the problem, and a hybrid algorithm based on an evolutionary algorithm and a heuristic approach is proposed to determine the optimal solutions. The case study has demonstrated the application of the algorithms and compared the results with the existing research. It has been found that the printing time can be reduced by as much as 41.3% based on the available hardware settings.