In this paper, a new green clustering algorithm is proposed to be as a first approach in the framework of an energy efficient strategy for centralized enterprise high-density WLANs. Traditionally, in order to maintain the network coverage, all the APs within the WLAN have to be powered-on. Nevertheless, the new algorithm can power-off a large proportion of APs while the coverage is maintained as its always-on counterpart. The two main components of the new approach are the faster procedure based on K-means and the more accurate procedure based on Evolutionary Algorithm (EA), respectively. The two procedures are processes in parallel for different designed requirements and there is information interaction in between. In order to implement the new algorithm, EA is applied to handle the optimization of multiple objectives. Moreover, we adapt the method for selection and recombination, and then introduce a new operator for mutation. This paper also presents simulations in scenarios modeled with ray-tracing method and FDTD technique, and the results show that about 67% to 90% of energy consumption can be saved while it is able to maintain the original network coverage during periods when few users are online or the traffic load is low.