This paper considers the Slepian-Wolf coding based energy minimization clustering (SWEMC) problem in a wireless sensor network (WSN), which aims to minimize the amount of data generated within each cluster and the overall energy cost for data transmission in the network. To solve the problem, we propose a Slepian-Wolf coding based energy-efficient clustering (SWEEC) algorithm, which is based on a heuristic algorithm for solving the minimum set weight cover problem in graph theory. The proposed SWEEC algorithm considers both the correlation structure of data from different sensor nodes and the distance of a cluster head to the sink(s) in cluster head election. Using this algorithm, a sensor node with a larger data compression rate and closer to the sink has a higher probability to become a cluster head. Simulation results show that the proposed SWEEC algorithm can significantly reduce the overall energy cost for data transmission and thus improve the energy efficiency of the network as compared with an existing Slepian-Wolf coding based clustering algorithm.