For beyond 5G era, in network function virtualization (NFV) environments, service chaining can be utilized to provide the flexible network infrastructures needed to support the creation of various application services. In this paper, we propose a dynamic service chain construction based on model predictive control (MPC) to utilize network resources. In the proposed method, the number of data packets in the buffer at each node is modeled as a dynamical system for MPC. Then, we formulate an optimization problem with the predicted amount of traffic injecting into each service chain from users for the dynamical system. In the optimization problem, the transmission route of each service chain, the node where each VNF is placed, and the amount of resources for each VNF are determined simultaneously by using MPC so that the amount of resources allocated to VNFs and the number of VNF migrations are minimized. In addition, the performance of data transmission is also controlled by considering the maximum amount of data packets stored in buffers. The performance of the proposed method is evaluated by simulation, and the effectiveness of the proposed method with different parameter values is investigated.