Multi-beam satellite networks can extend the service coverage as deploying the spot beams. It is important to allocate the appropriate resources to multi-beam downlinks to prevent the unnecessary waste of resources due to the inherent limitations of them, such as power, bandwidth, and even the use of a spot beam. In this paper, we propose a resource management technique adjusting the bandwidth of each beam, in which the difference between the traffic demand and allocated capacity is minimized. This represents a reasonable solution for flexible bandwidth allocation considering a trade-off between the maximum total capacity and fairness among the spot beams with different traffic demand. In addition, in order to improve the total system capacity, we present the flexible beam management algorithm. Meanwhile, the proposed flexible bandwidth allocation scheme does not yield a closed-form solution for the beam profile in terms of bandwidth. Therefore, we present the method to find optimal beam bandwidth via heuristic search.