Most studies on network function virtualization are based on cloud computing environments. Fog computing has been proposed as a supplement to cloud computing. When deploying the service function chain (SFC), the consumption of network resources can be effectively reduced by taking advantage of a combination of cloud and fog computing. However, few SFC studies are based on fog computing environments. Moreover, the problem of combining SFCs for the support of live online services to reduce network congestion and save network resources has not been considered. To effectively take advantage of cloud-fog computing and thus achieve the goal of saving resources and reducing network congestion, in this paper, we study the SFC combination and deployment problem in cloud-fog computing environments. To solve this problem, we present an efficient SFC combination and deployment algorithm. Finally, we conduct extensive simulations to evaluate the performance of our proposed algorithm. The results show that our proposed algorithm can effectively reduce network resource consumption and effectively resolve network congestion caused by live online services.