Fair packet sampling can obtain a higher packet sampling ratio of short flows by sacrificing the packet sampling of long ones; thus, ensuring better fairness among all flows than uniform random sampling does. However, the previously proposed fair sampling algorithm of Sketch Guided Sampling (SGS) has the drawbacks of poor space efficiency and large estimation error for short flows. In this paper, a space-efficient fair packet sampling (SEFS) algorithm is proposed. The key innovation of SEFS is a multi-resolution d-left hashing schema for flow traffic estimation. The performance of SEFS is compared to that of SGS in contexts of both flow traffic measurements and a long flow identification process that uses real-world traffic traces collected from OC-48 and OC-192 backbone network. The experimental results show that the proposed SEFS is more accurate than SGS in both application contexts, while a reduction of 65 percent in space complexity can be achieved. The improvement of estimation accuracy of SEFS is remarkable, especially for short flows, which comprise as past of a large percentage of whole network traffic flows.