Power efficiency of computer networks is an important issue for green computing. Currently available models such as the green pipe model minimizes the power consumption in the networks only for traffic demands which is fixed beforehand. In practice, the ongoing traffic demands can fluctuate due to different reasons, which the green pipe model cannot handle. On the contrary, some other existing models such as the green hose model can deal with traffic fluctuations, however with much lower power efficiency compared with the green pipe model. This research presents a robust green hoserectangle (green HR) model that employs the advantages of the mentioned both kinds of models. In one hand, our proposed model improves the power efficiency, on the other hand, allows the traffic demands to fluctuate within some acceptable range. In our model, we use an uncertainty set which is the intersection of the rectangle and hose uncertainty sets to allow errors and traffic fluctuations. Our model is tractable by modern optimization software within a reasonable time although it is in the form of mixed-integer linear programming (MILP) problem. Our experiments show some promising results. The efficiency of our proposed model is improved in terms of power savings, number of deactivating links, and computation time when compared with the green hose model