A constant-current control device for a power supply including a primary side switch and a secondary winding includes a voltage waveform detector, configured to generate a discharging period signal within a time length when the secondary winding is discharging according to a first feedback voltage and a control voltage; and a constant-current controller, wherein an integrator of the constant-current controller is configured to receive one of a first current source and a second current source according to the discharging period signal and a current detecting voltage to generate an integrator result voltage, wherein the current detecting voltage is related to a secondary winding current value flowing through the secondary winding and the secondary winding current value is positively related to a secondary output current value of the power supply.