Energy efficiency (EE) is a critical performance measure in the next generation wireless communication systems, especially for battery-constrained Internet of Things (IoT) devices. We investigate the power allocation optimization problem in a multi-channel wireless system for EE maximization, subject to the sum power and the throughput constraints over each group of assigned channels, as well as the total power constraint. Resorting to geometric interpretation on the constraints, we propose the group virtually ceiled and bottomed water-filling (GVC-WF) algorithm to solve this EE maximization problem. Our proposed algorithm computes the exact optimal solution with a quadratic polynomial computational complexity. With the optimality and computational advantages, our proposed algorithm is suitable for power allocation in large-scale wireless systems. Simulation results demonstrate that our proposed power allocation algorithm improves the energy efficiency by more than 40%, as compared to the conventional Dinkelbach’s method with the same amount of computations.