In this paper, a green and robust optimization model is proposed to the problem of minimizing network power consumption which can deal with uncertainty in traffic demands. The green pipe model achieves the first position in terms of minimizing network power consumption if we know the exact traffic demand. However, in reality, traffic demands fluctuate due to various situation. The hose model, which is formulated from the total outgoing/incoming amount of traffic from/to each node can allows errors in the traffic demands but its power consumption is higher than that of the green pipe model. Our proposed scheme is based on the green pipe model. For robust optimization, we use an uncertainty set which is the intersection of the hose and rectangle uncertainty set. The rectangle uncertainty set narrows the range of traffic conditions defined by the hose model by adding the upper and lower bounds for each source-destination pair in the network. In the worst case of traffic flow, we consider a subproblem and formulate the green hose-rectangle model (green HR) in the form of mixed-integer linear programming (MILP). Numerical results demonstrate that the problems obtained by the proposed green HR model can be solved by optimization software and reduce the network power consumption compare to the green hose model.