A resonant switching power converter includes: plural capacitors; plural switches; at least one charging inductor; at least one discharging inductor; a controller which generates a charging operation signal and at least one discharging operation signal; and at least one zero current detection circuit which detects a charging resonant current flowing through the charging inductor in a charging process and/or detect a discharging resonant current flowing through the discharging inductor in a discharging process. When detecting that a level of the charging resonant current or a level of the discharging resonant current is zero, the zero current detection circuit generates at least one zero current detection signal which is sent to the controller. The controller determines start time points and end time points of the charging process and the discharging process according to the zero current detection signal. There can be plural discharging processes.