In this letter, deep power control (DPC), which is the first transmit power control framework based on a convolutional neural network (CNN), is proposed. In DPC, the transmit power control strategy to maximize either spectral efficiency (SE) or energy efficiency (EE) is learned by means of a CNN. While conventional power control schemes require a considerable number of computations, in DPC, the transmit power of users can be determined using far fewer computations enabling real-time processing. We also propose a form of DPC that can be performed in a distributed manner with local channel state information, allowing the signaling overhead to be greatly reduced. Through simulations, we show that the DPC can achieve almost the same or even higher SE and EE than a conventional power control scheme, with a much lower computation time.