A pixel circuit and a driving method thereof, a display device are provided. The pixel circuit includes: a first thin film transistor, a second thin film transistor, a third thin film transistor, a fourth thin film transistor, a fifth thin film transistor, a sixth thin film transistor, a seventh thin film transistor, an eighth thin film transistor, a ninth thin film transistor, a first capacitor, a second capacitor, and a light emitting diode. In the pixel circuit provided by the embodiment of the application, a compensation voltage provided by a compensation voltage signal line can partially compensate a supply voltage during an emission stage of the pixel circuit.