The invention discloses a low-ripple soft-switching Cuk converter circuit and a modulation method, and belongs to the field of power electronics, and the low-ripple soft-switching Cuk converter circuit comprises a link energy storage capacitor C1, a resonant capacitor Cs, an output filter capacitor Co, a resonant branch diode Dax, main switching tubes Q1 and Q2, an auxiliary resonant switching tube Qax, an input inductor L1, an output inductor L2, a resonant inductor Lax and a coupling inductor M after the L1 and the L2 are coupled. The converter realizes zero-voltage conduction and zero-current turn-off of the main switch tube Q1, zero-voltage conduction of the main switch tube Q2 and zero-current turn-off of the anti-parallel diode DQ2 by controlling conduction and turn-off of the main switch tubes Q1 and Q2 and the auxiliary resonant switch tube Qax. The invention has the advantages that: 1) the output current ripple is small, and the power factor is high; 2) the link energy storage capacitor is designed in a critical conduction working mode, and a small-capacitance non-electrolytic capacitor can be used to replace an electrolytic capacitor; and 3) the soft switching function of main switching devices of the converter is realized, and the coupling inductance technology reduces the output ripple of the converter.