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Elephant flows contribute a large portion of the total traffic volume despite being relatively few in the number of flows. Thus, it is very important to identify these elephant flows in traffic engineering, network operation and management. One can easily keep counters for a few elephant flows using a small amount of fast memory (SRAM). Thus a reasonable goal is to devise an algorithm that identifies elephant flows using a limited SRAM memory. In this paper, we propose a novel approach to tackle this issue by using an identifying Elephant flows based on a Scalable Non-uniform Sampling algorithm (ESNS) to make the monitoring system self-adjustable to the varying monitored traffic. The paper use CERNET traces to compare the performance the ESNS algorithm with the sample and hold algorithm, and sampled algorithm. The experiment shows that the ESNS has better precision than PSH and sampled algorithm under the same flow memory size and configures.