Network function virtualization (NFV) technology significantly changes the traditional communication network environments by providing network functions as virtual network functions (VNFs) on commercial off-the-shelf (COTS) servers. Moreover, for using VNFs in a pre-determined sequence to provide each network service, service chaining is essential. A VNF can provide multiple service chains with the corresponding network function, reducing the number of VNFs. However, VNFs might be the source or the target of a cyberattack. If the node where the VNF is installed is attacked, the VNF would also be easily attacked because of its security vulnerabilities. Contrarily, a malicious VNF may attack the node where it is installed, and other VNFs installed on the node may also be attacked. Few studies have been done on the security of VNFs and nodes for service chaining. This study proposes a service chain construction with security-level management. The security-level management concept is introduced to built many service chains. Moreover, the cost optimization problem for service chaining is formulated and the heuristic algorithm is proposed. We demonstrate the effectiveness of the proposed method under certain network topologies using numerical examples.