One of the unique traffic features of low earth orbit (LEO) satellite networks is time-variant and nonuniform load distribution. This feature results in a locally biased congestion problem for the LEO satellite systems. In this paper, we propose a traffic load balancing scheme to resolve the congestion problem in such traffic scenarios. The proposing scheme makes use of near-neighbor residual bandwidth information to apportion excess bandwidth from congested satellites to their underloaded neighbors in the network. Each traffic load balancing process is performed on the domain basis. When the residual bandwidth of the path by way of the target satellite is less than a prespecified amount, calls routed over the path can be migrated to the alternative paths of the same balancing domain. By decreasing the size of the network graph being considered in load balancing process, balancing domains reduce the complexity of the process.