A pixel driving circuit, a driving method thereof, and a display device are provided. According to the pixel driving circuit, a data voltage is provided to a first electrode of a driving transistor; a storage sub-circuit is charged or discharged; a first voltage signal from a first voltage terminal is provided to a control electrode of the driving transistor, and a second voltage signal from a second voltage terminal or a third voltage signal from a third voltage terminal is provided to a first node; the data voltage and a threshold voltage of the driving transistor are written to the control electrode of the driving transistor, to turn on a second electrode of the driving transistor and the third voltage terminal, to control a light-emitting element to emit light.