Provided are a driving circuit and a driving method thereof, and a display device. The driving circuit includes a signal line, a control line, a driving unit, a power supply unit, a compensation unit, a light emitting control unit, a data writing unit, a storage unit, and an aging alleviation unit, wherein the driving unit is configured to drive a light emitting element; the light emitting control unit is configured to control the light emitting element to emit light; the data writing unit is configured to write the data signal into the storage unit; the compensation unit is configured to perform threshold voltage compensation for the driving unit; and the aging alleviation unit is configured to short-circuit a cathode and an anode of the light emitting element.