Network Function Virtualization (NFV) provides a good paradigm for sharing the resources of the physical network. The deployment problem of Service Function Chains (SFCs) composed of a specific order of Virtual Network Functions (VNFs) has become the focus of research. Moreover, to solve the facing challenges of the centralized cloud computing, the researchers have proposed the distributed fog computing. When the mobile user moves among different fog-based radio access networks, the SFC must be migrated. Therefore, in the paper, we research the problem of SFCs migration/remapping caused by the user movement in cloud–fog computing environments. We firstly model the migration problem of SFCs as an integer linear program; then we propose two SFC migration strategies: the minimum number of VNFs migration strategy and the two-step migration strategy, to reduce the reconfiguration cost, the migration time and downtime of SFCs and improve the remapping success ratio of SFCs; and we have designed a two-step migration algorithm to migrate SFCs. We use the cloud–fog computing environment to evaluate our proposed algorithms. The reconfiguration cost, the remapping success ratio, the migration time and the downtime of our proposed algorithms are more excellent than that of benchmark algorithm.