In a method for estimating a frequency offset (f.sub.e, .OMEGA..sub.e) of a modulated bandpass signal (s) with an assumed carrier frequency (.OMEGA..sub.0) in a mobile radio receiver, times (.tau..sub.j) of the zero cross-overs of the bandpass signal are determined in a first step. Using the times (.tau..sub.j) of the zero cross-overs and the assumed carrier frequency (.OMEGA..sub.0), the required frequency offset (f.sub.e, .OMEGA..sub.e) is estimated in a further step by calculating the DC component of an instantaneous frequency which is given by the frequency of the bandpass signal less the assumed carrier frequency.