Combining Network Functions Virtualization (NFV) with Software-Defined Networking (SDN) is an emerging solution to provide fine-grained control over scalable and elastic packet processing functions. Due to changes in network policy, traffic characteristics, or physical topology in Software-Defined NFV (SDNFV) systems, the controller needs to carry out network updates frequently, i.e., change the data plane configuration from one state to another. In order to adapt to a newly desired network state quickly, the network update process is expected to be completed in the shortest time possible. However, the update scheduling schemes need to address resource constraints including flow table sizes, CPU capacities of Virtualized Network Functions (VNFs) and link bandwidths, which are closely coupled. Thus, the problem is difficult to solve, especially when multiple flows are involved in the network update. In this work we investigate the multi-flow update problem in SDNFV systems, and formulate it as a mixed integer programming problem, which is NP-complete. We propose an approximation algorithm via linear relaxation. By extensive simulations, we demonstrate that our algorithm approaches the optimal solution, while requiring 10x-100x less computing time.