Combining Network Functions Virtualization (NFV) with Software-Defined Networking (SDN) is an emerging and promising solution to provide scalable and elastic network control and service. In such a system, virtualized Network Functions (NFs) need to be consistently migrated from one instance to another for various purposes, such as resource optimization, fault tolerance, load balancing, etc. These migrations involve simultaneously coordinating updates to the NF state and SDN forwarding state. To solve this problem, we design two consistent NF state update schemes: a controller-forwarding based scheme and a tagging-based scheme. Through analysis of the update process, we demonstrate that they both guarantee loss-free and order-preserving migrations. We further implement a prototype and carry out experiments with diverse traffic settings. Results demonstrate that the controller-forwarding based solution achieves 77 percent migration time compared with the state-of-the-art solution OpenNF, while correcting an error of it. Moreover, the tagging-based solution not only achieves 4.4 percent migration time, but also reduces up to 75 percent controller overhead compared with OpenNF at the cost of adding a tag in the unused fields of packet header.