The Internet needs to provide the diversified functions and services beyond simple packet forwarding for different network applications. It calls for supporting different communication demands with diversified and customized routing services. However, the current routing service configuration is not based on the global network information to manage network resources and functions, and cannot dynamically attain the adaptively and optimality. The Software Defined Networking (SDN) and Network Function Virtualization (NFV) have inspired a good way to solve these problems. In this paper, based on SDN and NFV, an Adaptive Routing Service Customization (ARSC) mechanism is proposed. In ARSC, the suitable routing services are adaptively customized for different applications with the user utility and the ISP profit considered jointly. In addition, in order to deal with the simultaneously arrived application requests, an efficient matching algorithm is devised to match different applications with appropriate candidate routing services. The matching is optimized with Pareto efficiency introduced, and the benefit equilibrium of the users and the ISPs can be achieved. Simulation results show that ARSC is feasible and effective.