The present disclosure provides a driving circuit and a driving method thereof, an array substrate, a display device, and a driving method thereof. The driving circuit is applied for driving a light-emitting element and a fingerprint detection element, and includes: a driving sub-circuit, outputting a light-emitting driving current to the light-emitting element under the control of a driving node; a data writing sub-circuit, communicating a data input terminal with the driving node in response to a scanning signal of a scanning signal terminal; a first energy storage sub-circuit, coupled to the driving node and a control signal terminal; a detection sub-circuit, outputting a detection current under the control of an output terminal of the fingerprint detection element; and a data output sub-circuit, outputting a detection current to the data output terminal in response to the scanning signal of the scanning signal terminal.