Switching power supply, and control circuit and method thereof

The invention discloses a switching power supply, and a control circuit and a control method thereof. The switching power supply converts an input voltage into an output voltage through switching on and switching off of the switch so as to provide the output voltage to a load. The control circuit uses an error amplification circuit to form a control loop to control on and off of the switch, and the error amplification circuit comprises a first input end, a second input end and an output end. The control circuit couples a first compensation resistance network between the first input terminal and the output terminal of the error amplification circuit or couples a second compensation resistance network at the first input terminal of the error amplification circuit. The control circuit also detects whether the switching power supply enters a transient state, and if the switching power supply enters the transient state, the first resistance value of the first compensation resistance network is increased or the sec