Generalized continuous wave synthetic aperture radar (GCW-SAR) is a promising new imaging radar system since it applies the full-duplex (FD) transmission technique to achieve continuous signaling in order to overcome several fundamental limitations of the conventional pulsed SARs. As in any FD wireless communication system, self-interference (SI) is also a key problem which can impact on the GCW-SAR system. In this paper, the analog least mean square (ALMS) loop in the radio frequency domain is adopted to cancel the SI for a GCW-SAR system with periodic chirp signaling. The average residual SI power after the ALMS loop is analyzed theoretically by a stationary analysis. It is found that the ALMS loop not only works with random signals in general FD communication systems, but also works well with the periodic signal in GCW-SAR systems. Simulation results show that over 45 dB SI cancellation can be achieved by the ALMS loop which ensures the proper operation of the GCW-SAR system.