It is known that software-defined networking (SDN) can support effective traffic engineering (TE) with the global view of networks. Hence, OpenFlow was used to realize flow-based TE. However, there is a tradeoff between the volume of installed flow entries and the granularity of TE. Moreover, the protocol-dependent nature of OpenFlow might limit the flexibility and adaptivity of TE. In this paper, we leverage the protocol-oblivious forwarding technology that can make each switch work as a protocol-independent white box and utilize its forwarding plane programmability to design a novel flexible flow converging (F-FC) scheme for realizing SDN-based fine-grained TE. Specifically, we design both the network system and the F-FC algorithms running on it and conduct experiments to demonstrate that our proposed scheme can not only reduce the volume of installed flow entries in switches but also realize fine-grained TE to achieve better utilization on network bandwidth.