Direct-conversion transceivers are in demand, due to their low cost implementation of analog front-ends. However, these transmitters or receivers introduce imperfections such as in-phase and quadrature-phase (I/Q) imbalances. These impairments can severely degrade the performance of cognitive radio devices that are based on orthogonal frequency division multiplexing (OFDM) multiple access schemes. In this paper, a cognitive radio system with an OFDMA primary system is considered. A new three-level hypothesis blind detector for spectrum sensing is introduced and the effect of I/Q imbalance on this detection scenario is studied. Finally, we show that the proposed detector is much less vulnerable to I/Q imbalance than conventional two-level detectors.