The battery charger comprises: two output terminals (BS1, BS2) between which a battery (102) is designed to be connected; two input terminals (BE1, BE2) designed to be connected to an electrical network (110); two inductors (L.A, L.C) respectively connected to the first input terminal (BE1) and to the second input terminal (BE2); two switching arms (BA, BC) for respectively connecting the inductors (LA, LC) selectively to the first output terminal (BS1) and to the second output terminal (BS2); a control device (120) designed for controlling the switching arms (BA, BC) so as to draw from the electrical network (110) a mains current (iR) in phase with the mains voltage (uR). The battery charger further comprises: a smoothing capacitor (C) connected to the second output terminal (BS2); and a connection device (112) for connecting the smoothing capacitor (C) to the second input terminal (BE2). The control device (120) is further designed to control at least the second switching arm (B.sub.C) so as to alternately charge and discharge the smoothing capacitor (C) for smoothing the load current (iB).