Circuit of wireless charging and method of charging battery

A circuit of wireless charging and a method of charging a battery. The circuit includes: a wireless receiver, configured to receive a charging power transmitted by a wireless transmitter of a wireless charging apparatus through electromagnetic induction; a charge pump circuit configured to receive a boosted input voltage from the voltage output end, and step down the input voltage to an output voltage of the charge pump circuit, to charge a battery; a step-down converter circuit configured to perform the step-down charging on the battery at least in a case that a charging mode is in a constant voltage mode; and a controller configured to select one between the charge pump circuit and the step-down converter circuit as a charging path to charge the battery based on a voltage difference between the input voltage from the voltage output end of the wireless receiver and a charging voltage of the battery.