In this paper a method to realize a heterodyne frequency-modulated continuous-wave (FMCW) radar is presented. The proposed principle relies on the use of an inphase/quadrature (IQ)-modulator as single-sideband-mixer to shift the frequency of the FMCW-output away from dc. Since in any IQ-modulator phase and amplitude imbalances occur, the effect of these imbalances will be investigated by deriving the corresponding signal model. Based on this analysis, a method to compensate the imbalances by a predistortion of the modulation signal will be derived. The presented method does not require special test signals or additional hardware, but relies on a standard FMCW measurement onto a calibration target. A prototype radar system was built and used in test measurements to verify the proposed principle. The measurement results show that a suppression of unwanted signal components caused by IQimbalances better than 45 dB is achievable.