Disclosed are an apparatus and method of diagnosing a failure of a switch element used to switch on or off external connection of a battery. The apparatus according to the present disclosure is an apparatus for diagnosing a failure of a switch element provided on a first line between a first electrode of a battery and a first external terminal, the apparatus including a current measuring unit configured to measure a current flowing through a second line between a second electrode of the battery and a second external terminal, a diagnosis resistor and a diagnosis switch provided on a third line to connect an outer node of the switch element and an outer node of the current measuring unit, and connected to each other in series, and a controller configured to apply a control signal for turning on or off the switch element, to the switch element, to turn on the diagnosis switch after the control signal is applied and then receive a measured current value from the current measuring unit, to determine a level of the current flowing through the second line, by using the measured current value, and to diagnose a failure of the switch element by comparing the current level to a reference current level.