In this article, we present a simple method to realize a sensor of ultrahigh sensitivity and compact size by employing a feedback double ring resonator. We demonstrate that this method has not only a higher sensitivity than an optimal add-drop resonator (ADR), but also a relatively high performance when the Q factor drops. Furthermore, we show that this sensing system can overcome the limitation of Q factor on system sensitivity by 2 orders of magnitude in comparison to the corresponding ADR. Thus, the proposal in this paper provides a promising and feasible scheme to realize a highly effective sensor that is weakly dependent on the Q factor of the system.