A pixel circuit and a driving method thereof, and a display device. The pixel circuit includes a driving circuit, a light emitting circuit, a fusing circuit and a fusing control circuit. The driving circuit is configured to convert a voltage signal input from a first voltage terminal into a driving current signal, and to output the driving current signal to the fusing circuit; the fusing circuit is configured to disconnect the light emitting circuit from the driving circuit; the fusing control circuit is configured to control the driving current signal to flow to the ground terminal under control of a signal input from the control line, to disconnect the light emitting circuit from the driving circuit; and the light emitting circuit is configured to emit light under control of the second voltage terminal in a case that the light emitting circuit is not disconnected from the driving circuit.