A method and an apparatus for digital up-down conversion using an Infinite Impulse Response (IIR) filter are provided. The method for digital up-down conversion for frequency conversion in a mobile communication system using plural frequency converts, includes IIR-filtering, by a magnitude response IIR filter having the same magnitude response as in Finite Impulse Response (FIR) filtering, an input signal and a stable filter coefficient calculated according to a Levinson polynomial; and receiving, by the magnitude response IIR filter, the IIR filtered signal, and performing IIR filtering by a phase compensation IIR filter having a filter coefficient compensating for a non-linear phase to a linear phase.