For the potential link congestion problem during traffic migration caused by IP network updates, a Congestion Avoidance and Fast Traffic Migration based on Multi-Topology Routing (CAFTM-MTR) algorithm was proposed. Firstly, the link capacity constraints and the timing characteristic of source node traffic migration were considered, and a congestion avoidance migration sequence that each moves one source node was gotten. Secondly, to shorten the migration finishing time, the algorithm was improved based on the sequence independence of traffics to make each batch move multiple sequence independent traffics. By using typical topologies and Waxman topologies to validate the proposed algorithm, the proposed algorithm improved the success rate of avoiding congestion from 20%-60% to 100% in the comparison experiments with Non-Congestion Avoidance and Fast Traffic Migration based on MTR (NonCAFTM-MTR) method, and obtained less than 8-round migration sequence. In addition, the proposed algorithm had an adaptability of dynamic traffic and was able to accommodate the traffic growth ranging from 5% to 284%. The simulation results show that CAFTM-MTR algorithm can effectively improve the success rate of congestion avoidance, and meanwhile make the traffic migration fast.