With network function virtualization (NFV) expanding from network center to edge, the service function chain (SFC) will gradually approach users to provide lower delay and higher-quality services. User mobility seriously affects the quality of service (QoS) provided by the mobile-aware SFC. Therefore, we must migrate the SFC to provide continuous services. In the user estimable movement scenario with a known mobile path and estimable arrival time, we establish the estimation model of user arrival time to obtain the estimated arrival time. Then, to reduce the time that the user is waiting for the migration completion, we propose a softer migration strategy migrating mobile-aware SFC before the user arrives at the corresponding access node. Moreover, for the problem of routing and bandwidth allocation (RBA), to reduce the migration failure rate, the paper proposes a path load adaptive routing and bandwidth allocation (PLARBA) algorithm adjusting the migration bandwidth according to the path load. The experimental results show that the proposed algorithm has significant advantages in reducing the user’s waiting time by more than 90%, decreasing migration failure rate by up to 75%, and improving QoS compared to the soft migration strategy and two RBA algorithms.