A peak power suppressing circuit can suppress a peak power of an IQ (In-phase and Quadrature-phase) baseband signal more assuredly. In particular, the peak power suppressing circuit performs a clipping process on an IQ baseband signal. The suppressing circuit includes a power calculation section that calculates an instantaneous power P of an IQ baseband signal, a pulse retention section that retains a cancellation pulse S that has a frequency component in a frequency band B of the IQ baseband signal and a frequency component outside the frequency band, and a clipping processing section that subtracts, from an IQ baseband signal whose instantaneous power P that has been calculated is greater than a predetermined threshold Pth, cancellation signals Ic and Qc obtained by multiplying increments ΔI and ΔQ of the IQ baseband signal from the threshold Pth by the cancellation pulse S.