A data clock frequency divider circuit includes a training decoder and a frequency divider. The training decoder outputs a clock alignment training signal, which is indicative of the start of a clock alignment training, in response to a command and an address of a mode register set. The frequency divider, which is reset in response to an output of the training decoder, receives an internal data clock to divide a frequency of the internal data clock in half. The data clock frequency divider circuit secures a sufficient operating margin so that a data clock and a system clock are aligned within a pre-set clock training operation time by resetting the data clock to correspond to a timing in which the clock training operation starts, thereby providing a clock training for a high-speed system.