Disclosed are an alternating current rectifying circuit and an alternating current rectifying method for driving an LED module. The method comprises: when an alternating current module is in a positive half cycle, after an alternating current output by the alternating current module is rectified, outputting the alternating current to a positive half cycle rectifying branch circuit of an external LED module; when the alternating current module is in a negative half cycle, carrying out charging according to the alternating current output by the alternating current module, and when the alternating current module is in the positive half cycle, carrying out discharging, and outputting the alternating current to a positive half cycle feed branch circuit of the external LED module; when the alternating current module is in the negative half cycle, rectifying the alternating current output by the alternating current module, and outputting the alternating current to a negative half cycle rectifying branch circuit of the external LED module; when the alternating current module is in the positive half cycle, carrying out charging according to the alternating current output by the alternating current module, and when the alternating current module is in the negative half cycle, carrying out discharging, and outputting the alternating current to a negative half cycle feed branch circuit of the external LED module. By using the present invention, stability of an output voltage can be improved, and luminous efficiency of the LED module can be improved.