The present invention is to provide a constant-current circuit capable of voltage compensation and zero-voltage switching, wherein the constant-current circuit is a single-switch isolated flyback converter and includes a control circuit, a sensing resistor, a transformer, a voltage divider, and a primary-side power switch. The control circuit obtains information related to a primary-side current of the transformer by way of the sensing resistor and obtains a compensation signal from an input voltage by way of the voltage divider, so as to control the primary-side power switch accordingly. Due to a compensating effect of the compensation signal, a peak voltage resulting from the sensing resistor is adjusted to a reference voltage through adding the compensation signal thereto, thereby enabling the constant-current circuit to generate a constant output current over a wide range of input voltage.