To decrease potentially harmful effects to the environment and reduce costs of cellular network operators, the exploration of energy saving is significant. In this paper, we shed light on the following energy consumption minimization (ECM) problem: “how to select the smallest set of active base stations (BSs) that can preserve the quality of service (the minimum data rate) required by the users.” Since the ECM problem belongs to the field of integer programming and is NP-hard, we propose two low-complexity approximation algorithms that yield performance guarantees: the iterative minimal set cover algorithm and the iterative maximal coverage (IMC) algorithm. Moreover, by leveraging the submodularity theory, we establish the performance bound of the IMC algorithm. Finally, the computational complexity of our proposed algorithms is analyzed, and a simulation platform is developed to evaluate the number of active BSs of proposed approaches. The numerical results demonstrate that our proposed algorithms outperform the conventional counterpart.