Because of the uneven distribution of the ground users and the LEO satellite movement, the rate of the LEO satellite network changes dramatically. And this will make the queue with limited buffer suffer from a large range of queue size oscillations, which would lead to high packet loss, low throughput etc. This paper proposes a rate-based stabilized BLUE algorithm. This algorithm uses the change of the average queue length to adjust the amount by which the mark (or drop) probability is changed; moreover it adjusts the queue weight, which is used to estimate the average queue length, based on the rate. Simulation results show that this algorithm could maintain higher throughput than BLUE algorithm as the rate of LEO satellite network changing dramatically.