A ferroelectric random access memory (FRAM) device and a driving method thereof are provided that reduce data loss in an operation of the FRAM device. A power supply supplies a power source to the memory device. A power detection circuit detects a voltage level of the power supply and generates a detection signal when the power source has an off state. In an internal chip enable (ICE) signal generation circuit, an ICE signal is disabled to stop operation of the memory device when the ICE signal is enabled and the detection signal is applied at a first time point, and an enabled state of the ICE signal is maintained when the detection signal is applied at a second time point, wherein the operation of the FRAM device continues by control signals generated from the ICE signal.