Cyber-physical Internet of things system (CPIoTS), as an evolution of Internet of things (IoT), plays a significant role in industrial area to support the interoperability and interaction of various machines (e.g. sensors, actuators, and controllers) by providing seamless connectivity with low bandwidth requirement. The fifth generation (5G) is a key enabling technology to revolutionize the future of industrial CPIoTS. In this paper, a communication framework based on 5G is presented to support the deployment of CPIoTS with a central controller. Based on this framework, multiple sensors and actuators can exchange information with the central controller in full-duplex mode. To accommodate the signal data in the available channel band, a resource allocation problem is formulated as a mixed integer non-convex programming problem, aiming to maximize the sum energy efficiency of CPIoTS. By introducing the transformation, we decompose the resource allocation problem into power allocation and channel allocation. Moreover, we consider an energy-efficient power allocation algorithm based on game theory and Dinkelbach's algorithm. Finally, to reduce the computational complexity, the channel allocation is modeled as a 3-dimensional matching problem, and solved by iterative Hungarian method with virtual devices (IHM-VD). A comparison is completed with well-known existing algorithms to demonstrate the performance of the proposed one. Simulation results confirm the efficiency of the proposed model, which significantly outperforms other benchmark algorithms in terms of meeting the energy efficiency and the QoS requirements.