According to the theory of a complex network, the overall characteristics are derived from complex interactions among its components, that is, network structure. For its service network, its overall characteristics are its functions. In view of the coordinated linkage between the 3D printing industry and the logistics industry, 3D printing is deeply integrated with Internet technology, digital casting technology and Internet + service platforms. We propose a hyper-network model of raw material suppliers, semi-finished product processors and finished product manufacturers that realize on-demand customization. To analyse, design, and build the cloud 3D printing manufacturing capability service competition network, we propose a 3D printing service node structure model based on a super network using a reference and cloud manufacturing service model. The model's mathematical structure is given in detail. Under this condition, it is necessary to discuss the interaction between the logistics service level, productivity level and product processing quantity. The process of the proposed model and method is given, and the validity is proven with a case study of a Cloud 3D printing service hyper-network in service-oriented manufacturing systems. INDEX TERMS Complex network, manufacturing resource services, service-oriented manufacturing (SOM), cloud manufacturing, cloud 3D printing, order-driven.