A service function chain (SFC) is an ordered virtual network function (VNF) chain for processing traffic flows to deliver end-to-end network services in a virtual networking environment. A challenging problem for an SFC in this context is to determine where to deploy VNFs and how to route traffic between VNFs of an SFC on a substrate network. In this paper, we formulate an SFC placement problem as an integer linear programing (ILP) model, and propose an availability-enhanced VNF placing scheme based on the layered graphs approach. To improve the availability of SFC deployment, our scheme distributes VNFs of an SFC to multiple substrate nodes to avoid a single point of failure. We conduct numerical analysis and computer simulation to validate the feasibility of our SFC scheme. The results show that the proposed scheme outperforms well in different network scenarios in terms of end-to-end delay of the SFC and computation time cost.