Embodiments of the present disclosure provide a drive circuit and a drive method thereof, a display substrate and a drive method thereof, and a display device. The drive circuit comprises a conversion unit provided with a first input terminal, a second input terminal, a third input terminal, a fourth input terminal, and an output terminal, wherein the fourth input terminal is connected to a direct current power source, and wherein the output terminal is connected to a pixel circuit. The first input terminal is configured to input a voltage signal, the second input terminal is configured to input a first drive signal, the third input terminal is configured to input a second drive signal, and the output terminal is configured to output a current signal. The conversion unit converts the voltage signal output from the source drive unit into the current signal and the pixel circuit is driven by the current signal.