Adaptive detection of radar target embedded in homogeneous Gaussian disturbance is addressed, by exploiting the persymmetric covariance matrix. On the basis of the decision schemes of generalised likelihood ratio test (GLRT), an adaptive persymmetric detector with constant false alarm rate property is designed, which can mitigate the demanding requirement of secondary data. Furthermore, the expressions for the probabilities of the false alarm and detection are derived, and the validity of them is confirmed by Monte Carlo simulations. The assessment results show that the proposed detector outperforms the conventional unstructured GLRT, the structured persymmetric adaptive matched filter and the persymmetric Rao detector, especially in the training‐deficient scenarios.