C-RAN presents an advanced mobile networking architecture that promises to tackle various challenging aspects of 5G such as increasing energy efficiency and providing high capacity. Indeed, C-RAN paves the way toward better energy efficiency by centralizing the baseband processing at cloud computing based servers (BBU pool). In this paper, we propose an RRH group based mapping (RGBM) that aims to minimize the power consumption at the BBU pool, while considering users’ QoS and BBU capacity constraints. To achieve this, the proposed scheme uses two key steps: i) the formation of RRH groups aimed at improving the QoS of weak users, ii) the formation of RRH cluster to be mapped for minimal number of BBUs requirement. The proposed scheme uses an efficient greedy heuristic to solve the optimization problem. The performance of the proposed approach was evaluated using simulations, which indicate a significant gain in terms of BBU minimization, power reduction and energy efficiency, while preserving QoS constraints, against well studied legacy solutions.