In one embodiment, a zero-crossing detection circuit for a synchronous step-down converter, can include: (i) a state determination circuit configured to compare a drain voltage of a synchronous transistor of the synchronous step-down converter against a reference voltage, and to generate a state digital signal indicative of whether a body diode of the synchronous transistor is turned on; (ii) a logic circuit configured to convert the state digital signal into a counting instruction signal; (iii) a plus-minus counter configured to generate a numerical signal in response to the counting instruction signal; (iv) a DAC configured to generate a correction analog signal based on the numerical signal; and (v) a zero-crossing comparator configured to receive the correction analog signal and the drain voltage of the synchronous transistor, and to provide a zero-crossing comparison signal to a driving circuit of the synchronous step-down converter.