Abstract: Traditional spectrum sensing schemes that are devised under the assumption of circular signals suffers from performance degradation in the presence of non-circular signals. To overcome such drawback, a novel spectrum sensing method for non-circular signals is proposed. Within the framework of generalized likelihood ratio, the test statistic is constructed by employing the nonzero characteristic of complementary covariance of non-circular signals. The proposed method is able to utilize the complete second-order statistical properties of non-circular signals, and does not require any prior information of the primary signals or noise power. Additionally, the statistical moments of proposed method are derived under null hypothesis, and the cumulative distribution function of proposed method is also obtained based on edgeworth expansion. On this basis, the analytic expression of sensing threshold is further established. Experimental results illustrate that the proposed method outperforms other state-of-the-art detectors in various scenarios.