A driving device and a driving method of a display panel are provided. The driving device includes a current source and a control circuit. The current source makes a driving current flow through a light-emitting element path of a sub-pixel circuit of the display panel. During a display line period, the driving current has a normal current amount, and the control circuit controls a first switch in the light-emitting element path to adjust a duty cycle of the driving current in the light-emitting element path. During a sensing period, the driving current has a sensing current amount less than the normal current amount, the control circuit turns on the first switch, and the control circuit checks a voltage in the light-emitting element path to determine whether a light-emitting element in the light-emitting element path is open (or whether the light-emitting element is provided in the light-emitting element path).