In recent years, the dense deployment of small base stations (SBSs) has led to the rising power consumption of mobile networks. In this paper, we introduce a convolutional neural network (CNN) based centralized sleeping control and bandwidth allocation (C-SCBA) scheme for multiple SBSs controlled by a central controller to minimize the total power consumption while satisfying the transmission rate requirements. We formulate the optimization problem as a mixed integer non-linear programming (MINLP) problem, and decouple it into two sub-problems: a centralized bandwidth allocation (CBA) sub-problem that minimizes the power consumption by optimizing the bandwidth allocation of the active SBSs; and a centralized sleeping control (CSC) sub-problem that finds the optimal SBS sleeping strategy among all the possible ones. The CBA sub-problem is transformed into a linear programming (LP) problem which can be directly solved by many existing software tools. For the CSC sub-problem, we transform it to a classification problem and propose CNN to solve it. Simulation results show that the proposed C-SCBA scheme has a near optimal performance in the reduction of total power consumption and satisfying the traffic requirments compared to the existing approaches in different situations.