The present disclosure provides a pixel driving circuit, a driving method thereof, and a display device. In one example, the pixel driving circuit includes: a driving transistor; a voltage holding sub-circuit, the first end of the voltage holding sub-circuit connected to the gate of the driving transistor; a data writing sub-circuit configured to supply a data voltage to the driving transistor when the first scanning line is at a first level, and connect the gate of the driving transistor and a second electrode; a converting sub-circuit configured to supply illumination power voltage to a second end of the voltage holding sub-circuit when the second scanning line is at the first level, and connect the second end of the voltage holding sub-circuit to the second end of the driving transistor when the third scanning line is at the first level; and a switch sub-circuit configured to supply illumination power voltage to the first end of the driving transistor when the third scanning line is at the first level, and connect the second end of the drive transistor to the current output end of the pixel drive circuit. The present disclosure can achieve threshold voltage compensation for the drive transistor.