A Light Emitting Diode (LED) driver apparatus is provided. The LED driver apparatus includes: a Pulse Width Modulation (PWM) signal generator configured to generate a PWM signal, a DC-DC converter configured to provide a driving voltage of a plurality of LED arrays by using the generated PWM signal, and a sensor configured to determine whether at least one LED array among the plurality of LED arrays is in an open state in response to the driving voltage being higher than or equal to a preset first reference voltage, and the preset first reference voltage is higher than the driving voltage applied when the plurality of LED arrays are each in a working state.