A computer having a monitor driving device for controlling video display turn-on time includes a power supply, a computer circuit, a monitor which may be integrated with the computer in one body, and a preheating controller. The monitor driving device for controlling video display time can reduce a time required for displaying a video image again without influencing the life span of a cathode ray tube when power is applied to use the monitor again after previously cutting off the power supplied to the monitor to reduce power consumption by the monitor which may be integrated with the computer in one body.