A cloud radio access network (C-RAN) is a promising network architecture to meet the explosive growth of the mobile data traffic. In this architecture, all the baseband signal processing is shifted to a single baseband unit (BBU) pool, which enables efficient resource allocation and interference management. Meanwhile, conventional powerful base stations can be replaced by low-cost low-power remote radio heads (RRHs), producing a green and low-cost network. However, as all the RRHs need to be connected to the BBU through backhaul links, the backhaul power consumption becomes significant and cannot be ignored. In this paper, we propose a new framework to design green C-RAN. Instead of only focusing on the RRH power consumption, we will minimize the network power consumption which includes the power consumed by both the RRHs and the backhaul links. The design problem is formulated as a joint RRH selection and power minimization beamforming problem, which turns out to be a convex-cardinality optimization problem and is NP-hard. We will first propose a global optimization algorithm based on the branch-and-bound method. By inducing the group-sparsity of the beamformers, we then propose two low-complexity algorithms, which essentially decouple the RRH selection and the power minimization beamforming. Simulation results demonstrate that the proposed algorithms can significantly reduce the network power consumption.